Contentsfile.etoosindia.com/sites/default/files/studymaterials/...Contents Syllabus Electrostatics...

Topic Page No.

Theory 01 - 02

Exercise - 1 03 - 14




Answer Key 37 - 37

Contents

SyllabusElectrostatics : Electricity and magnetism: Coulomb's law; Electric fieldand potential; Electrical Potential energy of a system of point charges andof electrical dipoles in a uniform electrostatic field, Electric field lines; Fluxof electric field; Gauss's law and its application in simple cases, such as,to find field due to infinitely long straight wire, uniformly charged infiniteplane sheet and uniformly charged thin spherical shell.

ELECTROSTATICS

Name : ____________________________ Contact No. __________________

ETOOSINDIA.COMIndia's No.1 Online Coaching for JEE Main & Advanced

3rd Floor, H.No.50 Rajeev Gandhi Nagar, Kota, Rajasthan 324005 HelpDesk : Tel. 092142 33303

www.etoosindia.com

www.etoosindia.com

ELECTROSTATICS # 1

List of formula for Electric Field Intensity due to various types of charge distribution :

KEY CONCEPT



www.etoosindia.com

ELECTROSTATICS # 2

Electric Potential due to various charge distributions are given in table.



www.etoosindia.com

ELECTROSTATICS # 3

PART - I : OBJECTIVE QUESTIONS

* Marked Questions are having more than one correct option.

Section (A) : Properties of charge and Coulomb's Law

A-1. A charged particle q1 is at position (2, - 1, 3). The electrostatic force on another charged particle q

2 at

(0, 0, 0) is :

(A) 0

21

56qq

)k�3j�i�2( (B) 0

21

1456

qq

)k�3j�i�2(

(C) 0

21

56qq

)k�3i�2j�( (D) 0

21

1456

qq

)k�3i�2j�(

A-2. Three charges +4q, Q and q are placed in a straight line of length at points at distance 0, /2 and respectively from one end of line. What should be the value of Q in order to make the net force on qto be zero?(A) �q (B) �2q (C) �q/2 (D) 4q

A-3. Two similar very small conducting spheres having charges 40 C and �20 C are some distance apart. Nowthey are touched and kept at same distance. The ratio of the initial to the final force between them is :(A) 8 : 1 (B) 4 : 1 (C) 1 : 8 (D) 1 : 1

A-4. Two point charges placed at a distance r in air exert a force F on each other. The value of distance R atwhich they experience force 4F when placed in a medium of dielectric constant K = 16 is :(A) r (B) r/4 (C) r/8 (D) 2r

Section (B) : Electric Field

B-1. There is a uniform electric field in X-direction. If the work done by external agent in moving a charge of 0.2C through a distance of 2 metre slowly along the line making an angle of 60º with X-direction is 4 joule,

then the magnitude of E is:

(A) C/N3 (B) 4 N/C (C) 5 N/C (D) 20 N/C

B-2. Charges 2Q and �Q are placed as shown in figure. The point at which electric field intensity is zero will

be:

(A) Somewhere between �Q and 2Q

(B) Somewhere on the left of �Q

(C) Somewhere on the right of 2Q(D) Somewhere on the right bisector of line joining �Q and 2Q

B-3. The maximum electric field intensity on the axis of a uniformly charged ring of charge q and radius R willbe :

(A) 04

1 2R33

q(B)

041

2R3

q2(C)

041

2R33

q2(D)

041

i 2R32

q3

B-4. A charged particle of charge q and mass m is released from rest in a uniform electric field E. Neglectingthe effect of gravity, the kinetic energy of the charged particle after time �t� seconds is

(A) t

Eqm(B)

m2tqE 222

(C) mq

tE2 22

(D) 2

2

t2

mEq



www.etoosindia.com

ELECTROSTATICS # 4

Section (C) : Electric Potential and Potential Difference

C-1. At a certain distance from a point charge, the electric field is 500 V/m and the potential is 3000 V.What is the distance ?(A) 6 m (B) 12 m (C) 36 m (D) 144 m

C-2. Figure represents a square carrying charges +q, +q, �q, �q at its four corners as shown. Then the

potential will be zero at points :

�q �qQ

A BC

+q+q

P

(A) A, B, C, P and Q (B) A, B and C (C) A, P, C and Q (D) P, B and Q

C-3. Two equal positive charges are kept at points A and B. The electric potential, while moving from A to Balong straight line :(A) continuously increases (B) remains constant(C) decreases then increases (D) increases then decreases

C-4. A semicircular ring of radius 0.5 m is uniformly charged with a total charge of 1.5 × 10�9 coul. Theelectric potential at the centre of this ring is :(A) 27 V (B) 13.5 V (C) 54 V (D) 45.5 V

C-5. When a charge of 3 coul is placed in a uniform electric field, it experiences a force of 3000 newton. Thepotential difference between two points separated by a distance of 1 cm along field within this field is:(A) 10 volt (B) 90 volt (C) 1000 volt (D) 3000 volt

C-6. A 5 coulomb charge experiences a constant force of 2000 N when moved between two points separatedby a distance of 2 cm in a uniform electric field. The potential difference between these two points is:(A) 8 V (B) 200 V (C) 800 V (D) 20,000 V

C-7. The kinetic energy which an electron acquires when accelerated (from rest) through a potential differenceof 1 volt is called :(A) 1 joule (B) 1 electron volt (C) 1 erg (D) 1 watt

C-8. The potential difference between points A and B in the given uniform electric field is :

aB

bE

E

C

A

(A) Ea (B) E )ba( 22 (C) Eb (D) )2/Eb(

C-9. An equipotential surface and an electric line of force :(A) never intersect each other (B) intersect at 45º

(C) intersect at 60º (D) intersect at 90º



www.etoosindia.com

ELECTROSTATICS # 5

C-10. A particle of charge Q and mass m travels through a potential difference V from rest. The final momen-tum of the particle is :

(A) Q

mV(B) mVQ2 (C) QVm2 (D)

mQV2

C-11. If a uniformly charged spherical shell of radius 10 cm has a potential V at a point distant 5 cm from itscentre, then the potential at a point distant 15 cm from the centre will be :

(A) 3V

(B) 3V2

(C) V23

(D) 3V

C-12. A hollow uniformly charged sphere has radius r. If the potential difference between its surface and apoint at distance 3r from the centre is V, then the electric field intensity at a distance 3r from the centreis:(A) V/6r (B) V/4r (C) V/3r (D) V/2r

C-13. A hollow sphere of radius 5 cm is uniformly charged such that the potential on its surface is 10 voltsthen potential at centre of sphere will be :(A) Zero(B) 10 volt(C) Same as at a point 5 cm away from the surface(D) Same as at a point 25 cm away from the centre

Section (D) : Electric Potential Energy of a Particle

D-1. If a charge is shifted from a high potential region to low potential region, the electrical potential energy:(A) Increases (B) Decreases(C) May increase or decrease. (D) Remains constant

D-2. A particle of mass 2 g and charge 1C is held at rest on a frictionless horizontal surface at a distanceof 1 m from a fixed charge of 1 mC. If the particle is released it will be repelled. The speed of the particlewhen it is at distance of 10 m from the fixed charge is:(A) 100 m/s (B) 90 m/s (C) 60 m/s (D) 45 m/s

Section (E) : Potential Energy of a system of Point Charge

E-1. When the separation between two charges is decreased, the electric potential energy of the charges(A) increases (B) decreases(C) may increase or decrease (D) remains the same

E-2. You are given an arrangement of three point charges q, 2q and xq separated by equal finite distancesso that electric potential energy of the system is zero. Then the value of x is :

(A) 32

(B) 31

(C) 32

(D) 23

E-3.* Which of the following quantites depends on the choice of zero potential or zero potential energy ?.(A) Potential at a particular point(B) Change in potential energy of a two-charge system(C) Potential energy of a two - charge system(D) Potential difference between two points

Section (F) : Self Energy and energy densityF-1. A sphere of radius 1 cm has potential of 8000 V. The energy density near the surface of sphere will be:

(A) 64 × 105 J/m3 (B) 8 × 103 J/m3 (C) 32 J/m3 (D) 2.83 J/m3

F-2. If ' n

' identical water drops (assumed spherical each) charged to a potential energy U coalesce to form

a single drop, the potential energy of the single drop is(Assume that drops are uniformly charged):(A) n1/3 U (B) n2/3 U (C) n4/3 U (D) n5/3 U



www.etoosindia.com

ELECTROSTATICS # 6

Section (G) : Questions based on relation between E

and V :

G-1.* The electric field intensity at a point in space is equal in magnitude to :(A) Magnitude of the potential gradient there(B) The electric charge there(C) The magnitude of the electric force, a unit charge would experience there(D) The force, an electron would experience there

G-2. The variation of potential with distance r from a fixed point is shown in Figure. The electric field at r = 5cm, is :

(A) (2.5) V/cm (B) (�2.5) V/cm (C) (�2/5) cm (D) (2/5) V/cm

G-3. In the above question, the electric force acting on a point charge of 2 C placed at the origin will be :(A) 2 N (B) 500 N (C) �5 N (D) �500 N

G-4. The electric potential V as a function of distance x (in metre) is given byV = (5x2 + 10x � 9) volt.

The value of electric field at x = 1 m would be :(A) � 20 volt/m (B) 6 volt/m (C) 11 volt/m (D) �23 volt/m

G-5. A uniform electric field having a magnitude E0 and direction along positive X-axis exists. If the electric

potential V is zero at x = 0, then its value at x = +x will be :(A) V

x = xE

0(B) V

x = �xE

0(C) V

x = x2E

0(D) V

x = �x2 E

0

G-6. Let E be the electric field and V, the electric potential at a point.(A) If E 0, V cannot be zero (B) If E = 0, V must be zero(C) If V = 0, E must be zero (D) None of these

Section (H) : DipoleH-1. Due to an electric dipole shown in fig., the electric field intensity is parallel to dipole axis :

(A) at P only (B) at Q only (C) both at P and at Q (D) neither at P nor at Q

H-2. An electric dipole of moment p is placed at the origin along the x-axis. The angle made by electric

field with x-axis at a point P, whose position vector makes an angle with x-axis, is :

(where, tan = tan21

)

(A) (B) (C) + (D) + 2



www.etoosindia.com

ELECTROSTATICS # 7

H-3. An electric dipole consists of two opposite charges each of magnitude 1.0 C, separated by a distance of2.0 cm. The dipole is placed in an external electric field of 1.0 × 105 N/C. The maximum torque on thedipole is :(A) 0.2 × 10�3 N-m (B) 1.0 × 10�3 N-m (C) 2.0 × 10�3 N-m (D) 4.0 × 10�3 N-m

H-4. A dipole of electric dipole moment P is placed in a uniform electric field of strength E. If is the anglebetween positive directions of P and E, then the potential energy of the electric dipole is largest when

is :(A) zero (B) /2 (C) (D) /4

H-5.* An electric dipole is placed (not at infinity) in an electric field generated by a point charge.(A) The net electric force on the dipole may be zero(B) The net electric force on the dipole will not be zero(C) The torque on the dipole due to the field may be zero(D) The torque on the dipole due to the field must be zero

H-6. At a point on the axis (but not inside the dipole and not at infinity) of an electric dipole(A) The electric field is zero(B) The electric potential is zero(C) Neither the electric field nor the electric potential is zero(D) The electric field is directed perpendicular to the axis of the dipole

H-7. The force between two short electric dipoles separated by a distance r is directly proportional to :(A) r2 (B) r4 (C) r�2 (D) r�4

Section (I) : Flux calculation and Gauss's law-1. A square of side 'a' is lying in xy plane such that two of its sides are lying on the axis. If an electric field

k�xEE 0

is applied on the square. The flux passing through the square is :�

(A) E0a3 (B)

2

aE 30 (C)

3

aE 30 (D)

2

aE 20

-2. If electric field is uniform, then the electric lines of forces are:(A) Divergent (B) Convergent (C) Circular (D) Parallel

-3. The figure shows the electric lines of force emerging from a charged body. If the electric fields at A andB are E

A and E

B respectively and if the distance between A and B is r, then :

B

A

(A) EA < E

B(B) E

A > E

B(C)

rE

E BA (D) 2

BA

r

EE

-4. Select the correct statement :(A) The electric lines of force are always closed curves(B) Electric lines of force are parallel to equipotential surface(C) Electric lines of force are perpendicular to equipotential surface(D) Electric line of force is always the path of a positively charged particle.



www.etoosindia.com

ELECTROSTATICS # 8

-5. If the electric flux entering and leaving a closed surface are respectively of magnitude 1 and 2 , then

the electric charge inside the surface will be :

(A) 0

12 �

(B) 021 )( (C) )�( 120 (D) )( 120

-6. An electric dipole is placed at the centre of a sphere. Mark the correct options.(A) The electric field is zero at every point of the sphere.(B) The flux of the electric field through the sphere is non-zero.(C) The electric field is zero on a circle on the sphere.(D) The electic field is not zero anywhere on the sphere.

-7. Figure (a) shows an imaginary cube of edge length L. A uniformly charged rod of length 2L movestowards left at a small but constant speed v. At t = 0, the left end of the rod just touches the centre ofthe face of the cube opposite to it. Which of the graphs shown in fig.(b) represents the flux of theelectric field through the cube as the rod goes through it ?

(a) (b)

b d a

c

time

Flux

(A) a (B) b (C) c (D) d

-8. Electric charges are distributed in a small volume. The flux of the electric field through a sphericalsurface of radius 20cm surrounding the total charge is 50 V-m. The flux over a concentric sphere ofradius 40 cm will be:(A) 50 V-m (B) 75 V-m (C) 100 V-m (D) 200 V-m

-9. Eight point charges (can be assumed as uniformly charged smallspheres and their centres at the corner of the cube) having value qeach are fixed at vertices of a cube. The electric flux through squaresurface ABCD of the cube is

(A) 024

q

(B) 012

q

(C) 06

q

(D) 08

q

-10. Figure shows two large cylindrical shells having uniform linear chargedensities + and � . Radius of inner cylinder is �a� and that of outer

cylinder is �b�. A charged particle of mass m, charge q revolves in a

circle of radius r. Then, its speed �v� is : (Neglect gravity and assume

the radii of both the cylinders to be very small in comparison to theirlength.)

(A) m2q

0

(B) m

q2

0

(C) mq

0

(D) m4

q

0

-11. A charge Q is placed at a distance of 4R above the centre of a disc ofradius R. The magnitude of flux through the disc is . Now ahemispherical shell of radius R is placed over the disc such that itforms a closed surface. The flux through the curved surface (takingdirection of area vector along outward normal as positive), is -(A) zero (B) (C) � (D) 2



www.etoosindia.com

ELECTROSTATICS # 9

Section (J) : Conductor, it's properties & Electric Pressure

J-1. A neutral spherical metallic object A is placed near a finite metal plate B carrying a positive charge. Theelectric force on the object will be :(A) away from the plate B (B) towards the plate B(C) parallel to the plate B (D) zero

J-2. A positive point charge q is brought near a neutral metal sphere.(A) The sphere becomes negatively charged.(B) The sphere becomes positively charged.(C) The interior remains neutral and the surface gets non-uniform charge distribution.(D) The interior becomes positively charged and the surface becomes negatively charged.

J-3. Three concentric conducting spherical shells carry charges as follows : + 4Q on the inner shell, - 2 Q onthe middle shell and � 5 Q on the outer shell. The charge on the inner surface of the outer shell is:(A) 0 (B) 4 Q (C) - Q (D) - 2 Q

J-4. A charge q is uniformly distributed over a large plastic plate. The electric field at a point P close to thecentre and just above the surface of the plate is 50 V/m. If the plastic plate is replaced by a copperplate of the same geometrical dimensions and carrying the same uniform charge q, the electric field atthe point P will become:(A) zero (B) 25 V/m (C) 50 V/m (D) 100 V/m

J-5.* A and B are two conducting concentric spherical shells. A is given acharge Q while B is uncharged. If now B is earthed as shown infigure.Then:

+ + ++++

++++++++ A

B

(A) The charge appearing on inner surface of B is -Q(B) The field inside and outside A is zero.(C) The field between A and B is not zero.(D) The charge appearing on outer surface of B is zero.

J-6. Figure shows a thick metallic sphere. If it is given a charge +Q, thenelectric field will be present in the region :(A) r < R

1 only

(B) r > R1 and R

1 < r < R

2

(C) r R2 only

(D) r R2 only

J-7. An uncharged sphere of metal is placed in a uniform electric field produced by two large conductingparallel plates having equal and opposite charges, then lines of force look like:

(A) (B) (C)

+

�

+ + + +

� � � �

(D)

J-8. Two small conductors A and B are given charges q1 and q

2 respectively.

Now they are placed inside a hollow metallic conductor (C) carrying acharge Q. If all the three conductors A, B and C are connected byconducting wires as shown, the charges on A, B and C will be respectively:

(A) Q,2

qq,

2qq 2121

(B) 3

qqQ,

3qqQ

,3

qqQ 212131

(C) 0,2

Qqq,

2Qqq 2121

(D) 0, 0, Q + q1 + q

2



www.etoosindia.com

ELECTROSTATICS # 10

J-9. You are travelling in a car during a thunder storm. In order to protect yourself from lightening, would youprefer to :(A) Remain in the car (B) Take shelter under a tree(C) Get out and be flat on the ground (D) Touch the nearest electrical pole

J-10. A positively charged body 'A' has been brought near a neutral brass sphere B mounted on a glassstand as shown in the figure. The potential of B will be:

(A) Zero (B) Negative (C) Positive (D) Infinite

J-11. The amount of work done in joules in carrying a charge +q along theclosed path PQRSP between the oppositely charged metal plates is:(where, E is electric field between the plates)(A) zero (B) q

(C) qE (PQ + QR + SR + SP) (D) 0/q

J-12. Figure shows a closed surface which intersects a conducting sphere. If a positive charge is placed atthe point P, the flux of the electric field through the closed surface:

(A) will become positive (B) will remain zero(C) will become undefined (D) will become negative

J-13. Two uniformly charged non-conducting hemispherical shells each having uniform charge density andradius R form a complete sphere (not stuck together) and surround a concentric spherical conductingshell of radius R/2. If hemispherical parts are in equilibrium then minimum surface charge density ofinner conducting shell is:(A) �2 (B) /2 (C) (D) 2

PART - II : MISCELLANEOUS QUESTIONS

Comprehensions

Comprehension # 1

A point charge q1 = +6e fixed at the origin of a coordinate

system, and another point charge q2 = � 10e is fixed at x = 8

nm , y = 0. The locus of all points in the xy plane for which

potential V= 0 (other than infinity)

is a circle centered on the x-axis , as shown.

xc q1 q2

y

x

Circle V=0

1. x-coordinate of the centre of the circle is -

(A) � 2nm (B) �3nm (C) �4.5nm (D) �7.5nm

2. Radius R of the circle is

(A) 3nm (B) 6nm (C) 7.5nm (D) 9nm

3. The potential at the centre of the circle is

(A) 0.32V (B) 0.77V (C) 1.2V (D) �1.2V



www.etoosindia.com

ELECTROSTATICS # 11

Comprehension # 2

A solid conducting sphere of radius �a� is surrounded by a thin uncharged concentric conducting shell of

radius 2a. A point charge q is placed at a distance 4a from common centre of conducting sphere and shell.

The inner sphere is then grounded.

a

2a

q4a

4. The potential of outer shell is.

(A) a32q

o(B) a16

q

o(C) a8

q

o(D) a4

q

o

5. The charge on solid sphere is :

(A) �2q

(B) 4q

(C) �8q

(D) �16q

6. Pick up the correct statement.

(A) Charge on surface of inner sphere is non-uniformly distributed.

(B) Charge on inner surface of outer shell is non-uniformly distributed.

(C) Charge on outer surface of outer shell is non-uniformly distributed.

(D) All the above statements are false.

Match the column

7. Column gives a situation in which two dipoles of dipole moment p i� and j� p 3 are placed at origin. A circle

of radius R with centre at origin is drawn as shown in figure. Column gives coordinates of certain positionson the circle. Match the statements in Column with the statements in Column .

pi�x

y

p j�3

R

Column Column

(A) The coordinate(s) of point on circle (p)

2R 3

, 2R

where potential is maximum :

(B) The coordinate(s) of point on circle where (q)

2R 3

, 2R

potential is zero :

(C) The coordinate(s) of point on circle where (r)

2R

,2

R 3

magnitude of electric field intensity is 30 R

p44

1

:

(D) The coordinate(s) of point on circle where (s)

2R

,2

R 3

magnitude of electric field intensity is 30 R

p24

1

:



www.etoosindia.com

ELECTROSTATICS # 12

8. Column gives certain situations involving two thin conducting shells connected by a conducting wire via akey K. In all situations, one sphere has net charge +q and other sphere has no net charge. After the key Kis pressed, column gives some resulting effects. Match the figures in Column with the statements inColumn .

Column Column

(A)

shell shell

+q

initially no net charge

K

(p) Charge flows through connecting wire

(B)

shell shell

+q initially no net chargeK

(q) Potential energy of system of spheres decreases.

(C)K

+q

shell

shell


(r) No heat is produced.

(D)

K

+q

shell

shell


(s) The shell has no charge after equilibrium is reached.



www.etoosindia.com

ELECTROSTATICS # 13

9. In each situation of column-I, some charge distributions are given with all details explained. In

column -II. The electrostatic potential energy and its nature is given situation in column -II. Then match

situation in column-I with the corresponding results in column-II and indicate your answer by darkening

appropriate bubbles in the 4 × 4 matrix given in the OMR.

Column-I Column-II

(A) A thin shell of radius a and having

a charge � Q uniformly distributed (p) aQ

81 2

0 in magnitude

over its surface as shown

(B) A thin shell of radius 2a5

and having

a charge � Q uniformly distributed (q) aQ

203 2

0 in magnitude

over its surface and a point charge

� Q placed at its centre as shown.

(C) A solid sphere of radius a and having

a charge � Q uniformly distributed (r) aQ

52 2

0 in magnitude

throughout its volume as shown.

(D) A solid sphere of radius a and having

a charge � Q uniformly distributed

throughout its volume. The solid sphere (s) Positive in sign

is surrounded by a concentric thin

uniformly charged spherical shell of

radius 2a and carrying charge �Q

as shown



www.etoosindia.com

ELECTROSTATICS # 14

10. In the shown figure the conductor is uncharged and a charge q is placed inside a spherical cavity at adistance a from its centre (C). Point P and charge +Q are as shown. a, b, c, d are known.

P

c

+Q

Cd

baq

Column-I Column-II(A) Electric field due to induced charges on (p) zero

the inner surface of cavity at point P

(B) Electric potential due to charges on the (q) non-zeroinner surface of cavity and q at P

(C) Electric field due to induced charges (r) value can be stated with the given data.on the outer surface of conductorand Q at C

(D) Electric potential due to induced charges (s) value cannot be stated from the given dataon the inner surface of cavity at C

PART - I : MIXED OBJECTIVE

Single Correct Answer Type.

1. A charged particle having some mass is resting in equilibrium at a height H above the centre of a uniformlycharged non-conducting horizontal ring of radius R. The force of gravity acts downwards. The equilibrium ofthe particle will be stable

(A) For all value of H (B) If H > 2

Ronly

(C) if H < 2

Ronly (D) If H =

2

Ronly

2. A circle of radius r has a linear charge density = 0 cos2 along its circumference. Total charge on the

circle is

(A) 0(2r) (B)

0(r) (C)

0 2

rFHGI

KJ (D)

0 4

rFHGI

KJ

3. A ring of radius (R) carries a uniformly distributed charge + Q. A point charge - q is placed on the axisof the ring at a distance 2R from the centre of the ring and released from rest . The particle :(A) Comes in rest condition immediately. (B) Executes simple harmonic motion

(C) Motion is not SHM (D) Comes at the centre of ring immediately.



www.etoosindia.com

ELECTROSTATICS # 15

4. A charge Q is kept at the centre of a conducting sphere of inner radius R1 and outer radius R

2. A point

charge q is kept at a distance r (> R2) from the centre. If q experiences an electrostatic force 10 N then

assuming that no other charges are present, electrostatic force experienced by Q will be:(A) � 10 N (B) 0 (C) 20 N (D) none of these

5. Two identical positive charges are fixed on the y-axis, at equal distances from the origin O. A particle with anegative charge starts on the x-axis at a large distance from O, moves along the + x-axis, passes through Oand moves far away from O. Its acceleration a is taken as positive along its direction of motion. Theparticle�s acceleration a is plotted against its x-coordinate. Which of the following best represents the plot?

(A) (B) (C) (D)

6. A mass particle (mass = m and charge = q) is placed bewteen two point charges of charge q separtionbetween these two charge is 2L. The frequency of oscillation of mass particle, if it is displaced for a smalldistance along the line joining the charges�

(A) 30Lm

12q

(B) 30Lm

42q

(C) 30Lm4

12q

(D)2

q3

0mL16

1

7. A charge Q is distributed over two concentric hollow spheres of radii (r) and (R) > (r) such that thesurface densities are equal. Find the potential at the common centre.

(A) 20 )rR(

)Rr(4

Q

(B) )Rr(4

)rR(Q

0

22

(C) )rR(4

)Rr(Q22

0

(D) none of these

8. A charge +q is fixed at each of the points x = x0, x = 3x

0, x = 5x

0 .... ad inf. on the x-axis, and a charge

� q is fixed at each of the points x = 2x

0, x = 4x

0, x = 6x

0 .... ad inf. Here x

0 is a positive constant. Take

the electric potential at a point due to a charge Q at a distance r from it to be Q/( r4 ). Then, the

potential at the origin due to the above system of charges is.

(A) Zero (B) 2logx8q

e00(C) (D)

00

e

x4

2logq

9. At any point ( x,0,0) the electric potential V is

32 x

500

x

1500

x

1000 volt, then electric field at

x = 1 m -

(A) m/V)k�j�(5500 (B) m/Vi�5500 (C) m/V)k�j�(2

5500 (D) m/V)k�i�(

2

5500

10. The equation of an equipotential line in an electric field is y = 2x, then the electric field strength vectorat (1, 2) may be :

(A) 4 3 i j (B) 4 8 i j (C) 8 4 i j (D) 8 4 i j



www.etoosindia.com

ELECTROSTATICS # 16

11. For an infinite line of charge having charge density lying along x-axis, the work required in movingcharge q from C to A along arc CA is :

(A) 0

q

log

e 2 (B)

04q

log

e 2 (C)

04q

log

e 2 (D)

02q

log

e 21

12. An isolated metallic object is charged in vacuum to potential v0, its electrostatic energy being W

0. It is

then disconnected from the source of potential, its charge being left unchanged and is immersed in alarge volume of dielectric, with dielectric constant k. The electrostatic energy will be.

(A) kW0

(B) 0W

k(C)

0

2

W

k(D) W

0.

13. The dipole moment of a system of charge +q distributed uniformly on an arc of radius R subtending an angle/2 at its centre where another charge -q is placed is :

(A)

qR22(B)

qR2(C)

qR(D)

qR2

Multiple Correct Answer(s) Type

14. Select the correct alternative :(A) The charge gained by the uncharged body from a charged body due to conduction is equal to half

of the total charge initially present.(B) The magnitude of charge increases with the increase in velocity of charge(C) Charge cannot exist without matter although matter can exist without charge(D) Between two non�magnetic substances repulsion is the true test of electrification (electrification

means body has net charge)

15.* A small sphere of mass m and having charge q is suspended by a light thread, then:(A) Tension in the thread may reduce to zero if anohter charged sphere is placed vertically below it.(B) Tension in the thread may increase to twice of its original value if another charged sphere is placed

vertically below it.(C) Tension in the thread is greater than mg if another charged sphere is held in the same horizontal

line in which first sphere stays in equilibrium.(D) None of these

16.* A large nonconducting sheet M is given a uniform charge density. Two uncharged small metal spheresA and B are placed near the sheet as shown in figure.

M

A B

(A) M attracts A (B) A attracts B (C) M attracts B (D) B attracts A



www.etoosindia.com

ELECTROSTATICS # 17

17.* Which of the following is true for the figure showing electric lines of force ? (E is electrical field, V is potential)

A B

(A) EA > E

B(B) E

B > E

A(C) V

A > V

B(D) V

B > V

A

18.* Which of the following quantities do not depend on the choice of zero potential or zero potential energy?

(A) Potential at a point.

(B) Potential difference between two points.

(C) Potential energy of a system of two charges.

(D) Change in potential energy of system of two charges.

19.* Three points charges are placed at the corners of an equilateral triangle of side L as shown in the figure.

(A) The potential at the centroid of the triangle is zero.�2q

LL

L+q +q

(B) The electric field at the centroid of the triangle is zero.

(C) The dipole moment of the system is 2qL

(D) The dipole moment of the system is 3qL .

20.* An electric dipole moment � �p (2.0i 3.0 j)

C. m is placed in a uniform electric field � �E (3.0i 2.0k)

× 105

N C�1.

(A) The torque that E

exerts on p

is � � �(0.6i 0.4 j 0.9k) Nm.

(B) The potential energy of the dipole is �0.6 J.

(C) The potential energy of the dipole is 0.6 J.

(D) If the dipole is rotated in the electric field, the maximum potential energy of the dipole is 1.3 J.

21.* A hollow closed conductor of irregular shape is given some charge. Which of the following statements are

correct?

(A) The entire charge will appear on its outer surface.

(B) All points on the conductor will have the same potential.

(C) All points on its surface will have the same charge density.

(D) All points near its surface and outside it will have the same electric intensity.

22. Three identical spheres each having a charge q and radius R, are kept in such a way that each touches

the other two. the magnitude of the electric force on any sphere due to other two is

(A) 2

0

31

4 4

q

R

(B) 2

0

21

4 4

q

R

(C) 2

0

21

4 4

R

q

(D) 2

0

31

2 4

q

R



www.etoosindia.com

ELECTROSTATICS # 18

PART - II : SUBJECTIVE QUESTIONS

1. Six charges are placed at the vertices of a regular hexagon as shown in the figure. Find the electric field onthe line passing through O and perpendicular to the plane of the figure as a function of distance x from pointO.

� Q

� Q

� Q

+ Q

+ Q

+ Q

a

O

2. A charge of 16 10-9 C is fixed at the origin of coordinates. A second charge of magnitude equal to(5X) × 10-9 C is at x = 3m, y = 0 and a third charge of 12 10-9 C is at x = 6m, y = 0. What is thevalue of the X if the resultant field at x = 8m, y = 0 is 20.25 N/C directed towards positive x-axis?

3. A spherical volume contains a uniformly distributed charge of density 2.0 × 10�4 C/m3 upto large distance.The electric field at a point inside the volume at a distance 4.0 cm from the centre is equal to X × 105

N/C. find value of X .

4. Two like charged, infinitely long wires with the same linear charge density of 10-8 C/cm are 2 mmapart. Find the electric force per unit length on each wire due to the other (in N/m)

5. A very long charged wire (lying in the xy plane) which is having a linear charge density 10-9 C/m ishaving one of its end and at a point P as shown in figure. What is electric field intensity (in N/C)at point

Q?(r=9 2 m)

6. A negatively charged particle with charge (�q) is moving around a fixed positive charge (+q) in a circular

path of radius R. The moving charge is shifted by an external agent so that it now moves in circular

motion of radius 2R around the fixed charge. The work done by the agent in doing so is 2Kq

X(R) .find value

7. You are given an arrangment of three point charges q, 2q and3Xq

separated by equal finite distances

so that electric potential energy of the system is zero. Calculate the value of x.

8. A spherical shell of radius R with uniform charge q is expanded to a radius 2R. The work performed

by the electric forces in this process is equal to 2

0

q4X R

.Find value of X



www.etoosindia.com

ELECTROSTATICS # 19

9. There are 27 drops of a conducting fluid. Each has radius r and they are charged to a potential V0=1 voltThey are then combined to form a bigger drop. Find its potential in volt.

10. The length of each side of a cubical closed surface is l. If charge q = 048 is situated on one of

the vertices of the cube, then find the flux passing through shaded face of the cube.q

11. Two thin conducting shells of radii R and 3R are shown in figure. The outer shell carries a charge +Q and theinner shell is neutral. The inner shell is earthed with the help of switch S. Find the magnitude of charge (incoulmb)attained by the inner shell.(take +Q = 3C).

+Q3R

R S

PART - I : IIT-JEE PROBLEMS (PREVIOUS YEARS)

* Marked Questions are having more than one correct option.

1. Which of the following groups do not have same dimensions [JEE 2005 (Scr.), 3 /60](A) Young�s modulus, pressure, stress

(B) Work, heat, energy(C) Electromotive force, potential difference, voltage(D) Electric dipole moment, electric flux, electric field

2. Three large parallel plates have uniform surface charge densities as shown in the figure. Find outelectric field intensity at point P. [JEE 2005 (Scr.), 3/60]

(A) �

0

4

k� (B)

0

4

k� (C) � k�

2

0

(D) k�

2

0

3. A bubble of conducting liquid is charged to potential V. It has radius a and thickness t << a. It collapsesto form a droplet. Find potential of the droplet. [ JEE 2005 (Mains), 2/60]



www.etoosindia.com

ELECTROSTATICS # 20

4.* For spherical symmetrical charge distribution, variation of electric potential with distance from centreis given in diagram. Given that : [JEE 2006 (Mains), 5/184]

V = 00R4

q

for r R0

and V = r4q

0 for r R

0.

Then which option(s) are correct :(A) Total charge within 2R

0 is q.

(B) Total electrostatic energy for r R0 is zero.

(C) At r = R0 electric field is dicontinuous.

(D) There will be no charge anywhere except at r = R0

5. A long hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinderof larger radius. Both the cylinders are initially electrically neutral. [JEE-2007, 3/184](A) A potential difference appears between the two cylinders when a charge density is given to the

inner cylinder.(B) A potential difference appears between the two cylinders when a charge density is given to the

outer cylinder.(C) No potential difference appears between the two cylinders when a uniform line charge is kept

along the axis of the cylinders.(D) No potential difference appears between the two cylinders when same charge density is given

to both the cylinders.

6. Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. Then thenet charge on the sphere is : [JEE-2007, 3/184](A) negative and distributed uniformly over the surface of the sphere.(B) negative and appears only at the point on the sphere closest to the point charge.(C) negative and distributed non-uniformly over the entire surface of the sphere.(D) zero.

7. A spherical portion has been removed from a solid sphere having a charge distributed uniformlyin its volume as shown in the figure. The electric field inside the emptied space is :

[JEE-2007, 3/184]

(A) zero every where (B) is not zero but uniform(C) nonuniform (D) is zero at centre only

8. Positive and negative point charges of equal magnitude are kept at

2a

,0,0 and

2a

,0,0 ,

respectively. The work done by the electric field when another positive point charge is movedfrom (�a, 0, 0) to (0, a, 0) is [JE-2007, 3/184](A) positive(B) negative(C) zero(D) depends on the path connecting the initial and final positions.



www.etoosindia.com

ELECTROSTATICS # 21

9. Consider a system of three charges 3q

, 3q

and 3q2

placed at points A, B and C, respectively, as shown in

the figure. Take O to be the centre of the circle of radius R and angle CAB = 60º. [JEE-2008, 3/163]

(A) The electric field at point O is 20 R8

q

directed along the negative x-axis.

(B) The potential energy of the system is zero.

(C) The magnitude of the force between the charges at C and B is 20

2

R54

q

.

(D) The potential at point O is R12q

0.

Paragraph for Question Nos. 10 to 12

The nuclear charge (Ze) is non�uniformly distributed within a nucleus of radius R. The charge density (r)[charge per unit volume] is dependent only on the radial distance r from the centre of the nucleus as shownin figure. The electric field is only along the radial direction. [JEE-2008 ; 12/163]

10. The electric field at r = R is :(A) independent of a (B) directly proportional to a(C) directly proportional to a2 (D) inversely proportional to a

11. For a = 0, the value d (maximum value of as shown in the figure) is :

(A) 3

2

R4

Ze3

(B) 3R

Ze3

(C) 3R3

Ze4

(D) 3R3

Ze

12. The electric field within the nucleus is generally observed to be linearly dependent on r. This implies :

(A) a = 0 (B) a = 2R

(C) a = R (D) a = 3R2



www.etoosindia.com

ELECTROSTATICS # 22

13. STATEMENT -1 [JEE -2008, 3, �1/163]For practical purposes, the earth is used as a reference at zero potential in electrical circuits.andSTATEMENT -2The electrical potential of a sphere of radius R with charge Q uniformly distributed on the surface is given by

R4Q

0.

(A) STATEMENT -1 is True, STATEMENT -2 is True; STATEMENT -2 is a correct explanationfor STATEMENT -1

(B) STATEMENT -1 is True, STATEMENT -2 is True; STATEMENT -2 is NOT a correct explanation forSTATEMENT -1

(C) STATEMENT -1 is True, STATEMENT -2 is False(D) STATEMENT -1 is False, STATEMENT -2 is True.

14. A disk of radius a/4 having a uniformly distributed charge 6C is placed in the x-y plane with its centre at(�a/2, 0, 0). A rod of length a carrying a uniformly distributed charge 8C is placed on the x-axis from x = a/4

to x = 5a/4. Two point charges �7C and 3C are placed at (a/4, �a/4, 0) and (�3a/4, 3a/4, 0), respectively.

Consider a cubical surface formed by six surfaces x = ± a/2, y = ± a/2, z = ±a/2. The electric flux through this

cubical surface is : [JEE -2009, 3/160, �1]

(A) 0

C2

(B)

0

C2

(C) 0

C10

(D) 0

C12

15. Three concentric metallic spherical shells of radii R, 2R, 3R, are given charges Q1, Q2, Q3, respectively. It isfound that the surface charge densities on the outer surfaces of the shells are equal. Then, the ratio of thecharges given to the shells, Q1 : Q2 : Q3, is [JEE -2009, 3/160, �1](A) 1 : 2 : 3 (B) 1 : 3 : 5 (C) 1 : 4 : 9 (D) 1 : 8 : 18

16. Under the influence of the Coulomb field of charge +Q, a charge �q is moving around it in an elliptical orbit.

Find out the correct statement(s). [JEE -2009, 4/160, �1](A) The angular momentum of the charge �q is constant.

(B) The linear momentum of the charge �q is constant.

(C) The angular velocity of the charge � q is constant.

(D) The linear speed of the charge �q is constant.

17. A solid sphere of radius R has a charge Q distributed in its volume with a charge density = kra, where k and

a are constants and r is the distance from its centre. If the electric field at r = 2R

is 81

times that at r = R, find

the value of a. [JEE -2009, 4/160, �1]



www.etoosindia.com

ELECTROSTATICS # 23

18.* A few electric field lines for a system of two charges Q1 and Q2 fixed at two different points on the x-axis areshown in the figure. These lines suggest that : [JEE-2010, 3/163]

(A) |Q1| > |Q2|(B) |Q1 | < |Q2|(C) at a finite distance to the left of Q1 the electric field is zero(D) at a finite distance to the right of Q2 the electric field is zero

19. A uniformly charged thin spherical shell of radius R carries uniform surface charge density of per unit area.It is made of two hemispherical shells, held together by pressing them with force F (see figure). F is proportionalto [JEE-2010, 5/163, �2]

F F

(A) 22

0

R1

(B) R

1 2

0

(C) R1 2

0

(D) 2

2

0 R

1

20. A tiny spherical oil drop carrying a net charge q is balanced in still air with a vertical uniform electric field of

strength 5107

81

Vm�1. When the field is switched off, the drop is observed to fall with terminal velocity

2 × 10�3 m s�1. Given g = 9.8 m s�2, viscosity of the air = 1.8 × 10�5 Ns m�2 and the density of oil = 900 kgm�3, the magnitude of q is : [JEE-2010, 5/163, �2](A) 1.6 × 10�19 C (B) 3.2 × 10�19 C (C) 4.8 × 10�19 C (D) 8.0 × 10�19 C

21. Consider an electric field 0 �E E x, where E0 is a constant. The flux through the shaded area (as shown in

thefigure) due to this field is : [JEE-2011]

(A) 2E0a

2(B) 2

02E a (C) E0a2 (D)

20E a

2

22.* A spherical metal shell A of radius RA and a solid metal sphere B of radius R

B (< R

A) are kept far apart and

each is given charge �+Q�. Now they are connected by a thin metal wire. Then : [JEE-2011]

(A) 0EinsideA (B) Q

A > Q

B(C)

A

B

B

A

RR

(D) On surface On surface

A BE E



www.etoosindia.com

ELECTROSTATICS # 24

23. A wooden block performs SHM on a frictionless surface with frequency, 0. The block carries a charge + Q

on its surface. If now a uniform electric field E

is switched-on as shown, then the SHM of the block will be :

[JEE-2011]

(A) of the same frequency and with shifted mean position.(B) of the same frequency and with same mean position.(C) of changed frequency and with shifted mean position.(D) of changed frequency and with the same mean position.

24.* Which of the following statement(s) is/are correct? [JEE-2011](A) If the electric field due to a point charge varies as r �2.5 instead of r �2, then the Gauss law will still be

valid.(B) The Gauss law can be used to calculate the field distribution around an electric dipole.(C) If the electric field between two point charges is zero somewhere, then the sign of the two charges is

the same.(D) The work done by the external force in moving a unit positive charge from point A at potential V

A to

point B at potential VB is (V

B � V

A).

25. Four point charges, each of +q, are rigidly fixed at the four corners of a square planar soap film of side �a�The surface tension of the soap film is . The system of charges and planar film are in equilibrium, and

a = k

1/N2q

, where �k� is a constant. Then N is [JEE-2011]

26. Two large vertical and parallel metal plates having a separation of 1cm are connected to a DC voltage sourceof potential difference x. A proton is released at rest midway between the two plates. It is found to move, at45° to the vertical. JUST after release. Then x is nearly [JEE-2012](A) 1 × 10�5 V (B) 1 × 10�7 V (C) 1 × 10�9 V (D) 1 × 10�10 V

27. Consider a thin spherical shell of radius R with its centre at the origin, carrying uniform positive surface

charge density. The variation of the magnitude of the electric field E(r)

and the electric potential V(r) with

the distance r from the centre, is best represented by which graph ? [JEE-2012]

(A) (B)

(C) (D)



www.etoosindia.com

ELECTROSTATICS # 25

28.* A cubical region of side a has its centre at the origin. It encloses three fixed point charges, �q at (0, �a/4,0),

+3q at (0,0,0) and �q at (0, +a/4,0). Choose the correct option(s).

[JEE-2012]

(A) The net electric flux crossing the plane x = +a/2 is equal to the net electric flux crossing the plane

x = �a/2.

(B) The net electric flux crossing the plane y = +a/2 more than the net electric flux crossing the plane

y = �a/2.

(C) The net electric flux crossing the entire region is 0

q

.

(D) The net electric flux crossing the plane z = +a/2 is equal to the net electric flux crossing the plane

x = +a/2.

29. An infinitely long solid cylinder of radius R has a uniform volume charge density . It has a spherical cavity of

radius R/2 with its centre on the axis of the cylinder, as shown in figure. The magnitude of the electric field at

the point P which is at a distance 2R from the axis of the cylinder, is given by the expression 0

23 R16k

. The

value of k is [JEE-2012]



www.etoosindia.com

ELECTROSTATICS # 26

PART - I : AIEEE PROBLEMS (PREVIOUS YEARS)

1. A charged ball B hangs from a silk thread S, which makes an angle with a large charged conducting sheetP, as shown in the figure. The surface charge density of the sheet is proportional to: [AIEEE-2005, 4/300]

S

P

++++++++++

(1) sin (2) tan (3) cos (4) cot

2. Two point charges + 8 q and � 2q are located at x = 0 and x = L respectively. The location of a point on the

x axis at which the net electric field due to these two point charges is zero is: [AIEEE-2005, 4/300](1) 8L (2) 4L (3) 2L (4) L/4

3. Two thin wire rings, each having a radius R are placed at a distance d apart with their axes coinciding. Thecharges on the two rings are + q and �q. The potential difference between the centers of the two rings is:

[AIEEE-2005, 4/300]

(1) zero (2) 04

qðå

22 dR

1R1

(3) 20d4

qR

ðå (4) 02

qðå

22 dR

1R1

4. An electric dipole is placed at an angle of 30o to a non-uniform electric field. The dipole will experience[AIEEE-2006, 4/220]

(1) A torque as well as a translational force.(2) A torque only.(3) A translational force only in the direction of the field.(4) A translational force only in a direction normal to the direction of the field.

5. Two insulating plates are both uniformly charged in such a way that the potential difference between them isV2 - V1 = 20 V. (i.e. plate 2 is at a higher potential). The plates are separated by d = 0.1 m and can be treatedas infinitely large. An electron is released from rest on the inner surface of plate 1. What is its speed when ithits plate 2? (e = 1.6 × 10-19 C, me = 9.11 × 10-31 kg) [AIEEE-2006, 4/220]

(1) 1.87 × 106 m/s (2) 32 × 10-19 m/s (3) 2.65 × 106 m/s (4) 7.02 × 1012 m/s



www.etoosindia.com

ELECTROSTATICS # 27

6. Two spherical conductors A and B of radii 1 mm and 2mm are separated by a distance of 5 cm and areuniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratioof the magnitude of the electric fields at the surfaces of sphere A and B is : [AIEEE-2006, 4/220](1) 2 : 1 (2) 1 : 4 (3) 4 : 1 (4) 1 : 2

7. An electric charge 10�3µC is placed at the origin (0,0) of X�Y co-ordinate system. Two points A and B are

situated at 2,2 and (2,0) respectively. The potential difference between the points A and B will be

[AIEEE-2007, 3/120](1) 9 volt (2) zero (3) 2 volt (4) 4.5 volt

8. Charges are placed on the vertices of a square as shown. Let E

be the electric field and V the potential at thecentre. If the charges on A and B are interchanged with those on D and C respectively, then :

[AIEEE-2007, 3/120]

(1) E

remains unchanged, V changes (2) Both E

and V change

(3) E

and V remain unchanged (4) E

changes, V remains unchanged

9. The potential at a point x (measured in µm) due to some charges situated on the x-axis is given by

V(x) = 20/(x2 � 4) volts. The electric field E at x = 4 m is given by : [AIEEE-2007, 3/120](1) 5/3 volt/µm and in the �ve x direction (2) 5/3 volt/µm and in the +ve x direction

(3) 10/9 volt/µm and in the �ve x direction (4) 10/9 volt/µm and in the +ve x direction

10. A thin spherical shell of radius R has charge Q spread uniformly over its surface. Which of the followinggraphs most closely represents the electric field E (r) produced by the shell in the range 0 < r < , where ris the distance from the centre of the shell? [AIEEE-2008, 3/105]

(1) (2) (3) (4)

11. Two points P and Q are maintained at the potentials of 10 V and �4 V respectively. The work done in moving

100 electrons from P to Q is : [AIEEE-2009, 4/144](1) 9.60 × 10�17 J (2) �2.24 × 10�16 J (3) 2.24 × 10�16 J (4) �9.60 × 10�17 J

12. A charge Q is placed at each of the opposite corners of a square. A charge q is placed at each of the othertwo corners. If the net electrical force on Q is zero, then Q/q equals: [AIEEE-2009, 4/144]

(1) �1 (2) 1 (3) 2

1 (4) � 22

13. Statement 1 : For a charged particle moving from point P to point Q, the net work done by an electrostaticfield on the particle is independent of the path connecting point P to point Q. [AIEEE-2009, 6/144]Statement 2 : The net work done by a conservative force on an object moving along a closed loop is zero.(1) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.(2) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.(3) Statement-1 is false, Statement-2 is true.(4) Statement-1 is true, Statement-2 is false.



www.etoosindia.com

ELECTROSTATICS # 28

14. Let (r) = rR

Q4

be the charge density distribution for a solid sphere of radius R and total charge Q. For a

point �P� inside the sphere at distance r1 from the centre of sphere, the magnitude of electric field is:[AIEEE-2009, 4/144]

(1) 210r4

Q

(2) 4

0

21

R4

Qr

(3) 4

0

21

R3

Qr

(4) 0

15. A thin semi-circular ring of radius r has a positive charge q distributed uniformly over it. The net field E

at thecentre O is : [AIEEE-2010, 4/144]

(1) j�r4

q2

02åð (2) � j�

r4

q2

02åð (3) � j�

r2

q2

02åð (4) j�

r2

q2

02åð

16. Let there be a spherically symmetric charge distribution with charge density varying as

Rr

45

)r( 0ññ

upto r = R, and (r) = 0 for r > R, where r is the distance from the origin. The electric field at a distance r(r < R) from the origin is given by [AIEEE-2010, 4/144]

(1)

Rr

35

3

r4

0

0

åðñ

(2)

Rr

35

4

r

0

0

åñ

(3)

Rr

45

3

r4

0

0

åñ

(4)

Rr

45

3

r

0

0

åñ

17. Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 30º

with each other. When suspended in a liquid of density 0.8 g cm�3, the angle remains the same. If density ofthe material of the sphere is 1.6 g cm�3, the dielectric constant of the liquid is [AIEEE-2010, 8/144](1) 4 (2) 3 (3) 2 (4) 1

18. The electrostatic potential inside a charged spherical ball is given by = ar2 + b where r is the distance fromthe centre; a, b are constant. Then the charge density inside the ball is : [AIEEE-2011, 4/144](1) �24a0r (2) �6a0r (3) �24a0 (4) �6a0

19. Two identical charged spheres suspended from a common point by two massless strings of length areinitially a distance d(d << ) apart because of their mutual repulsion. The charge begins to leak from both thespheres at a constant rate. As a result the charges approach each other with a velocity v. Then v as a functionof distance x between them,(1) v x�1/2 (2) v x�1 (3) v x1/2 (4) v x

20. In a uniformly charged sphere of total charge Q and radius R, the electric field E is plotted as function ofdistance from the centre. The graph which would correspond to have above will be : [AIEEE-2012, 4/120]

(1) (2) (3) (4)



www.etoosindia.com

ELECTROSTATICS # 29

21. This questions has statement-1 and statement-2. Of the four choice given after the statements, choose theone that best describe the two statements.Statement-1 : When a charge 'q' is take from the centre of the surface of the sphere its potential energy

changes by 03

q

.

Statement-2 : The electric field at a distance r ( r < R) from the centre of the sphere is 03r

.

[AIEEE-2012, 4/120](1) Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.(2) Statement-1 is true Statement-2 is false.(3) Statement-1 is false Statement-2 is true.(4) Statement-1 is true, Statement-2 is true, Statement-2 is the correct explanation of Statement-1.

PART - I : BOARD PATTERN QUESTIONS

1. Is electric field a conservative force? Give reasons for your answer.

2. While measuring an electric field, why do we always use a very small charge as the test charge?

3. Describe the electric field lines of a uniform positive line charge.On a positive line charge, the electric field lines are pointed radially-outward at each point.

4. An electric field exists in a region given by the equation:

What is the electric flux through area which lies in the xy plane?

5. What is a 'dipole'? How is an electric dipole moment defined?

6 . A uniform electric field exists in a region (as shown below). In this region, a cone is placed such that its axisis perpendicular to the direction of the electric field.

What is the electric flux that enters from the left hand side of the cone?

7. A thin and long straight wire has a linear charge density?. Derive an expression of the electric field at adistance r from the wire.

8. (a) Show that an electric dipole, kept at some angle with the direction of a uniform electric field, experiencesa zero net force.

(b) Derive the expression for torque, acting on the dipole, placed in a uniform electric field.



www.etoosindia.com

ELECTROSTATICS # 30

9.

A bob of mass m with a charge � q is set to oscillation. The time period recorded followed the equation:

Now, a uniform electric field E is applied (as shown in the given figure). Obtain a formula for calculating thetime period in the above case.

10. (a) Define the dipole moment of an electric dipole. Give its S.I. unit.(b) Derive an expression for the electric field at a point on the axis of the dipole.

11. (a) 'q' amount of positive charge is spreadout evenly throughout the volume of a conducting sphere (as shownin the figure below).

How do these charges behave thereafter?(b) Derive an expression for the electric field intensity at a point:i. Inside the sphereii. Outside the sphereiii. Surface of the sphere

12. What is the work done in moving a charge +4 ?C through distance of 2 m on an equipotential surface?

13. Why can two equipotential surfaces never intersect?

14. The number of electrons in a given charged sample is equal to the Avogadro number. Calculate the work donein moving this sample through a potential difference of 5 V.

15. How does the electric field in a region change, if a dielectric of dielectric constant 'K' is introduced in theregion?

16. A uniform electric field exists in a region (as shown in the given figure).

How much work is done in taking an electron from A to C on path ABC?

17. A uniform electric field exists along the x ?axis. In what direction can a charge be displaced so that no workis done in displacing it ?



www.etoosindia.com

ELECTROSTATICS # 31

18. (a) An electron is 20 cm away from a fixed point charge, Q = � 0.250 C. If it starts to move from rest, thenhow fast will it be moving when it is at a distance?(b) How much work is done in bringing three electrons, which are initially a great distance apart, to form an

equilateral triangle with sides

19. (a) A metallic sphere of radius 0.2 m is given a 4 C charge. Calculate the electric potential at a distanceof 0.05 m from the centre of the metallic sphere.

(b) Three concentric, spherical shells P, Q, and R of radii 4 cm, 6 cm, and 8 cm are given charges of 2 C,

4 C, and 6 C respectively (as shown in the figure below). Calculate the net electric potential at P,Q,and R respectively.

PART-II NCERT QUESTIONS

1.

2.

3.

4.

5.

6.

7. (a) An electrostatic field line is a continuous curve. That is, a field line cannot have sudden breaks. Why not?(b) Explain why two field lines never cross each other at any point?



www.etoosindia.com

ELECTROSTATICS # 32

8.

9.

10.

11.

12.

13.

14.



www.etoosindia.com

ELECTROSTATICS # 33

15.

16.

17.

18. A point charge +10 C is a distance 5 cm directly above the centre of a square of side 10 cm, as shown infigure. What is the magnitude of the electric flux through the square? (Hint:Think of the square as one face ofa cube with edge 10 cm.)

19.

20.

21.

22.



www.etoosindia.com

ELECTROSTATICS # 34

23.

24.

25.

26. Which among the curves shown in figure cannot possibly represent electrostatic field lines?

(a) (b) (c)

(d) (e)

27.



www.etoosindia.com

ELECTROSTATICS # 35

28. (a) A conductor A with a cavity as shown in figure (a) is given a charge Q. Show that the entire charge mustappear on the outer surface of the conductor. (b) Another conductor B with charge q is inserted into the cavitykeeping B insulated from A. Show that the total charge on the outside surface of A is Q + q [figure (b)]. (c) Asensitive instrument is to be shielded from the strong electrostatic fields in its environment. Suggest apossible way.

29.

30.

31.

32.

33.

34.



www.etoosindia.com

ELECTROSTATICS # 36

35.

36.

37.

38.

39.

40.





www.etoosindia.com

ELECTROSTATICS # 37

41.

42.

43.

44.



www.etoosindia.com

ELECTROSTATICS # 38

Exercise # 1PART-I

A-1. (D) A-2. (A) A-3. (A) A-4. (C) B-1. (D) B-2. (B) B-3. (C)

B-4. (B) C-1. (A) C-2. (B) C-3. (C) C-4. (A) C-5. (A) C-6. (A)

C-7. (B) C-8. (C) C-9. (D) C-10. (C) C-11. (B) C-12. (A) C-13. (B)

D-1. (C) D-2. (B) E-1. (C) E-2. (A) E-3.* (AC) F-1. (D) F-2. (D)

G-1.* (AC) G-2. (A) G-3. (D) G-4. (A) G-5. (B) G-6. (D) H-1. (C)

H-2. (C) H-3. (C) H-4. (C) H-5.* (BC) H-6. (C) H-7. (D) I-1. (B)

I-2. (D) I-3. (B) I-4. (C) I-5. (C) I-6. (D) I-7. (D) I-8. (A)

I-9. (C) I-10. (A) I-11. (C) J-1. (B) J-2. (C) J-3. (D) J-4. (C)

J-5.* (ACD) J-6. (C) J-7. (C) J-8. (D) J-9. (A) J-10. (C) J-11. (A)

J-12. (A) J-13. (A)PART-II

1. (C) 2. (C) 3. (B) 4. (A) 5. (B) 6. (C)

7. (A) p (B) r,s (C) p,q (D) r,s 8. (A) p, q (B) p, q (C) p, q, s (D) r, s

9. (A) p, s (B) q, s (C) q, s (D) s 10. (A) q, s (B) p, r (C) p, r (D) q, r

Exercise # 2PART-I

1. (B) 2. (B) 3. (C) 4. (B) 5. (B) 6. (A) 7. (C)

8. (D) 9. (B) 10. (D) 11. (A) 12. (B) 13. (A) 14.* (CD)

15.* (ABC) 16.* (BD) 17.* (AD) 18.* (BD) 19.* (AD) 20.* (ABD) 21.* (AB)

22. (AC)PART-II

1. 0 2. 5 3. 3 4. 9 6. 4 7. 2 8. 4

9. 9 10. 2 11. 1

Exercise # 3PART-I

1. (D) 2. (C) 3. V = V

3/1

t3a

4.* (ABCD) 5. (A)

6. (D) 7. (B) 8. (C) 9. (C) 10. (A) 11. (B) 12. (C)

13. (B) 14. (A) 15. (B) 16. (A) 17. 2 18.* (A*D) 19. (A)

20. (D) 21. (C) 22.* (ABCD) 23. (A) 24.* (CD) 25. 3

26. (C) 27. (D) 28.* (ACD) 29. 6

PART-II1. (2) 2. (3) 3. (4) 4. (1) 5. (3) 6. (1) 7. (2)8. (4) 9. (4) 10. (4) 11. (3) 12. (4) 13. (1) 14. (2)15. (3) 16. (2) 17. (3) 18. (4) 19. (1) 20. (3) 21. (3)



www.etoosindia.com

Contentsfile.etoosindia.com/sites/default/files/studymaterials/...Contents Syllabus Electrostatics...

Documents

Transcript of Contentsfile.etoosindia.com/sites/default/files/studymaterials/...Contents Syllabus Electrostatics...