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1
Welcome to Electromagnetism
Ed Copeland
Arundel [email protected]
http://www.pact.cpes.susx.ac.uk/users/edmundjc/emg_course.htm
I am very grateful to Professor Dam Waddill for making his
slides available to me for this course.
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Some details:
Lectures: Tue 11.30 and Thur 9.15 : Pev1-1A6.
Workshop: Tue 18.00 : Pev1-1A1.
Problem sheets: Hand in Monday following
relevant workshop.
Essay: Handed in first weds after Easter break.Office hour: Thur 15.00: Arundel 205
Course Book: Tipler,Physics for Scientists and
Engineers, 4th edition.
All details to be found at:
http://www.pact.cpes.susx.ac.uk/users/edmundjc/emg_course.htm
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Electric Charge and Electric Field
Todays menu Properties of Electric Charges
Insulators and Conductors Coulombs Law
The Electric Field
The Electric Dipole
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Electric Charges Two kinds of charges: Positive and Negative
Like charges repel - unlike charges attract Charge is conserved and quantized
1909 Robert Millikan : electric charge always occurs in integral
multiples of the fundamental unit of charge, e.
Q is the standard symbol for charge (units-Coulombs)
Q = Ne ; e = 1.602 x 10-19 C,N is an integer
Proton charge: + e : Electron charge: - e :Neutron charge: 0
Quarks charge : 1/3 e or 2/3 e How come?
Never find isolated individual quarks
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Insulators and Conductors
Classify materials according to their ability toconduct electrical charge.
Conductors: free moving charge (metal)
Insulators: charge not readily transported (wood)
Semiconductors: electrical properties between
conductor and insulator (silicon)
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Coulombs Law1785 Charles Coulomb : fundamental law of electric
force between two stationary charged particles. It is:
inversely proportional to square of separation betweenparticles
directed along the line joining the particles
proportional to the product of the two charges attractive if particles have charges of opposite sign
and repulsive if charges have same sign
1 212 2
e
Q QF k rr
=r
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1 212 2
e Q QF k rr
=r
F12 is the force on charge Q2 due to Q1 and
is the unit vector pointing from Q1 to Q2r is the distance between Q1 and Q2ke is Coulombs constant and has a value of
8.988 x 109N.m2/C2
r
1Q
2Q
r
rrrr r
r
=
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Coulombs constant ke in terms of thepermittivity of free space 0.
-12 2 2
0
18.85 10 C /N m
4 ek
= =
1 212 2
0
1 4
Q QF rr
=r
1 212 2
e
Q QF k rr
=r
Coulombs law can be written as :
or
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1 212 2
M M
F G r
r
= r
1 212 2
e
Q QF k r
r
=r
Coulomb ForceGravitational Force
Lets compare
Attractive or repulsive Only attractive
36
g
c
27
p
2211
19229
2proton
2
g
c
1024.1F
Fkg1067.1m;kgNm1067.6G
C106.1e;CNm1099.8k
protons2forGm
ke
F
F
=
==
==
=
Why dont we worry about electric forces for macroscopic bodies?
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Reminder of direction of Coulomb Force
+
+
1
1
1
+
2
2
2
F21
F21
F12
F12
F12
F21
Recall F12 is force on charge 2 due to charge 1
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Superposition Principle vital!
When more than two charges are present:
resultant force on any one of them is equal to the
vector sum of the forces exerted by each of the
individual charges.
1 21 31 41F F F F= + + +r r r r
L
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+
+
+
0.5 m
0.5 m
Q2
Q1
0.3 m
0.3 m
y
0.4 m
F23
Q3 F13
x
Example 1
3 point charges Q1 = Q2 = 2 Cand Q3 = 4 C are arranged as
shown. Find the resultant force on
Q3
.
( )1 3
13 20.5 m
e
Q QF k=
( )
6 69
13 2
(2.0 10 )(4.0 10 )(9.0 10 ) 0.29 N
0.5
F
= =
( )2 3
23 1320.5m
e
Q QF k F= =
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+
+
+
0.5 m
0.5 m
Q2
Q1
0.3 m
0.3 m
y
0.4 m
F23
Q3 F13
x
Continuation of Example 1
3 point charges Q1 = Q2 = 2 Cand Q3 = 4 C are arranged as
shown. Find the resultant force on
Q3
.
13 0.29NF = 23 13F F=
13 13
13 13
( ) cos
( ) sin
x
y
F F
F F
=
=
0.4cos 0.8
0.50.3
sin 0.60.5
= =
= =
13 23 13 23
13
( ) ( ) cos cos
2 cos 2(0.29)(0.8) 0.46 N
x x x
x
F F F F F
F F
= + = +
= = =
13 23
13 23
( ) ( )
sin sin 0 N
y y y
y
F F F
F F F
= +
= + =
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The Electric Field
Useful when describing a force that acts at a distance.
Electric field at some point in space is defined as the
electric force acting on a positive test charge, q0, placed
at that point divided by the magnitude of the test charge.
It is a vector quantity with units of N/C.
0
FEq
=
r
r
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For point charges:
+
Q
q0
F
r
r
-
Q
q0F
r
r
0
2
2
0 0
e
e
Qqk r
F QrE k rq q r
= = =
r
r
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Superposition principle for Electric FieldsIf the field is due to more than one charge then the
individual fields are added vectorially (superposition
principle).
1 2 3 4 ...E E E E E= + + + +r r r r r
For a series of point charges the electric field is:
2i
e i
i i
QE k r
r=
r
ri is the distance from the ith charge to the point ofevaluation
is a unit vector from the ith charge to the point of
evaluation, and Qi is the ith
charge.
ir
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+ x
Q1 Q2
0.6 m
0.5 m 0.5 m
P
y
E2
E1
Example 2
Charges Q1 and Q2 are placed 0.6 m apart. Q1 = +5 C
and Q2 = -5 C. Find the electric field at pointP.
61 9 5
1 2 2 2
1
5.0 10(9.0 10 ) 1.8 10 N/C
(0.5)e
QE E k
r
= = = =
1 2
1 2
1
cos cos
2 cos
x x x
x
x
E E E
E E E
E E
= +
= +
=
0.3cos 0.6
0.5 = =
5 52(1.8 10 )(0.6) 2.2 10 N/CxE = =
1 2
1 2sin sin 0 N/C
y y y
y
E E E
E E E
= +
= =
( )5
2.2 10 N/C
x yE E i E j
E i
= +
=
r
r
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Electric dipoles Electric dipole is a system of two
equal and opposite charges Q a
small distanceL apart
Electric dipole moment,p, is
vector pointing from negative to
positive charge with magnitudegiven byp=QL.
If L is displacement vector of
positive charge from negativecharge, dipole moment is
+
-Q Q
L
p=QL
LQpr
r
=
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Example 3y
x-Q +Q
-a aGiven two opposite charges at a, and a, findelectric field and dipole moment on the x-axis
at a field point P which is a large distance
away compared to 2a.
P
1. Point P is a dist (x-a) from positive and dist (x+a) from neg charges.
2. Electric field at point P due to the two charges is:
i)ax(
axkQ4
i)ax(
)Q(k
i)ax(
kQ
E 22222
rrrr
=+
+=
3. For x>>a, can neglect a2 compared to x2 in the denominator.
Electric field at P is: ix
kaQ4
E 3
rr
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3. For x>>a, can neglect a2 compared to x2 in the denominator.
Electric field at P is: ix
kaQ4E
3
rr
4. Electric Dipole Moment Displacement is: iaQ2pia2Lr
rrr
==
Hence magnitude of E on x axis of the dipole a great distance
away from it is :
3x
kp2E=
Thus the electric field far from a dipole is proportional to the
dipole moment and decreases with the cube of the distance.
