swati on magnetic effect of current

7/31/2019 swati on magnetic effect of current

1/18

1

We can find the direction of magnetic field by using right hand rule. Asshown in the picture above, grab the wire with your four fingers, your

thumb shows the direction of current and four fingers show the directionof magnetic field.

Example: Two currents flow through the x and y axis of the wire. Asyou can see from the picture two points are located near the wires A andB. If the total magnetic field at Ais BA, and total magnetic fieldat B is BB, find ratio ofBA/BB?


2/18

2

Magnetic field at point B;


3/18

3

Introduction Biot-Savart Law (Magnetic Field due to a Current) Magnetic Field due to a Straight (infinitely) long Current

Carrying wire

Magnetic Field due to a circular current loop Current Loop and Magnetic Dipole Force Law Forces on Currents and the Lorentz force Ampere's Circuital Law Moving Charge in Electric Field

Galvanometer

CONTENTS
http://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/magnetic_effect_intro.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/magnetic_effect_intro.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/biot_savart.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/biot_savart.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/magnetic_field_due_to_straight.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/magnetic_field_due_to_straight.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/magnetic_field_due_to_straight.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/magnetic_field_due_to_straight.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/magnetic_field_due_to_straight.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/magnetic_field_due_to_circular_loop.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/magnetic_field_due_to_circular_loop.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/current_loop_n_mag_dipole.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/current_loop_n_mag_dipole.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/forces_laws.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/forces_laws.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/lorentz_force.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/lorentz_force.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/ampere_circuital_law.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/ampere_circuital_law.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/moving_charges_in_electric_field.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/moving_charges_in_electric_field.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/galvanometer.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/galvanometer.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/galvanometer.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/moving_charges_in_electric_field.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/ampere_circuital_law.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/lorentz_force.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/forces_laws.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/current_loop_n_mag_dipole.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/magnetic_field_due_to_circular_loop.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/magnetic_field_due_to_straight.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/magnetic_field_due_to_straight.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/biot_savart.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/magnetic_effect_intro.htm


4/18

4

The elementary source of magnetic force is a small length dl (or a length element)

of a conductor carrying a current I. The force on another similar conductor can beexpressed conveniently in terms of a magnetic field dB due to the first. Thedependence of such magnetic field on the current I, on the size and orientation ofthe line element d1, and on the distance r from it was guessed atby Biot and Savart from measurements on finite (not infinitesimal) current-carrying wires with simple shapes, e.g. lines, rectangles and circles. Thesemeasurements were of forces as well as comes equilibrium near such wires. Thisdirection turns out to be that of the total resultant magnetic field, i.e., the vectorsum of the magnetic fields due to the current-carrying wire and the earth.

The magnitude of the magnetic field dB at a distance r from a currentelement dl carrying a current I is found to be proportional to I, to the length dl andinversely to the square of the distance |r|. The direction of the magnetic field isperpendicular to the line element dl as well as the radius r.

oI dl x r

dB = ------- --------- tesla (Wb/m2)4p r3
http://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/biot_savart.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/biot_savart.htm


5/18

5

Consider a straight infinitely long wire carrying a steady current I. The lineAP is perpendicular to the wire, and is of length R. From theBiot-Savart law, themagnetic field dB due to a small element dl of the wire near the point O at adistance |r| = r from P (OP=r) is

o I dl x rdB = ------- ---------

4p r3

Since the current element dl and the vector r make an angle q with each other, the

product dl*r has a magnitude dlr sin q. It is directed perpendicular to both dl andr. This is the direction perpendicular to the plane of the paper and going into it, asis clear from the right handed corkscrew rule (link) (direction of advance of a righthanded corkscrew turning from dl to r).

o I dl sin qdB = ---- -------k

4 p r2

The magnetic field at a point P due to a infinite (very long) straight wire

carrying a current I is proportional to I, and is inversely proportional to theperpendicular distance R of the point from the wire. The integral J has a value of2, so that
http://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/biot_savart.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/biot_savart.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/biot_savart.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/electricity/electricity/effects_of_current/magnetic_field_due_to_straight.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/electricity/electricity/effects_of_current/magnetic_field_due_to_straight.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/electricity/electricity/effects_of_current/magnetic_field_due_to_straight.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/electricity/electricity/effects_of_current/magnetic_field_due_to_straight.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/biot_savart.htm


6/18

6

The field dB due to a small element dl of the circle, centered at A has themagnitude

o Idl o IdldB= ----- ------- = ---- ---------

4 p |AP|2 4 p (R2 + a2)

This field can be resolved into two components one along the axis OP, and theother (PS) perpendicular to it. The latter component is exactly cancelled by theperpendicular component (PS) of the field due to a current and centred at A.

Field along OP has a magnitude

oI dldB (along OP) = ---- ----{in }

4 p r2

o Idl a= --- --------------

4 p R2 + a2 (R2 + a2)1/2

o Ia= --- -------dl

4 p (R2 + a2)3/2


7/18

7

The magnetic field due to the circular current loop of radius a at a point whichis a distance R away, and is on its axis (i.e. on a line perpendicular to the plane ofthe circle and passing through its center) is

oa2

B = i (i is the unit vector along OP, the x-axis) tesla (Wb/m2)

o B = k tesla (Wb/m2)

2 R

(R2 + a2)3/2


8/18

8

Current carrying conductors exert forces on each other Suppose the magneticfield at a particular point is B. The force on a small current carrying wire dl

situated at that point is found to be

dF = I dl x B newton

Where I is the electric current passing through the small conductingsegment. This is the magnetic analogue of the electric force law F = qE we noticethat the force proportional to I, dl and B and is perpendicular to both dl and B.


9/18

9

The fundamental force on an electric charge q moving with velocity v in amagnetic field B is called the magnetic Lorentz force.

F N = I (l x B) = N q v x B

Where Nq is the total electrical charge in the current-carrying conductor,drifting with velocity v.

The total force (often calledLorentz force) on a charge q moving with

velocity v in an electric field E and magnetic field B is

F = q ( E + v x B )
http://www.ncert.nic.in/html/learning_basket/electricity/electricity/electricity/electricity/effects_of_eurrent/lorentz_force.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/electricity/electricity/effects_of_eurrent/lorentz_force.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/electricity/electricity/effects_of_eurrent/lorentz_force.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/electricity/electricity/effects_of_eurrent/lorentz_force.htm


10/18

10

If charges (each of charge q) drift in the conductor with aspeed v, the current I is

I = n q A v

Here A is the cross-sectional area of the conductor and there are n charges perunit volume. If the current is carried by electrons, as happens most often, thecharges q is just the electric charge e on an electron, and the actual direction ofdrift of electrons is opposite to that of the current, i.e. v is negative if I ispositive. Suppose the current flows in a straight conductor l place in a uniformmagnetic field B.

I | l | = I l + [ nAl ] qv

The quantity in square brackets above is just the number N of charges in thelength l, since its volume is |Al| and the number density of charges is n. We thushave

I l =Nqv

Theforce equationcan be then rewritten as

F N = I (l x B) = N qv x B

This fundamental force on an electric charge q moving with velocity v in amagnetic field B is called the magnetic Lorentz force.

EXPLAINATION
http://www.ncert.nic.in/html/learning_basket/electricity/electricity/electricity/electricity/effects_of_current/explanation_lorentz.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/electricity/electricity/effects_of_current/explanation_lorentz.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/electricity/electricity/effects_of_current/explanation_lorentz.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/forces_laws.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/forces_laws.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/forces_laws.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/electricity/electricity/effects_of_current/explanation_lorentz.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/electricity/electricity/effects_of_current/explanation_lorentz.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/electricity/electricity/effects_of_current/explanation_lorentz.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/forces_laws.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/electricity/electricity/effects_of_current/explanation_lorentz.htm


11/18

11

The total force (often called Lorentz force) on a charge q moving withvelocity v in an electric field E and magnetic field B is

F = q ( E + v * B ) newton

The magneticLorentz forceis perpendicular to both the velocity v (or thedirection of motion) and magnetic field B.
http://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/lorentz_force.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/lorentz_force.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/lorentz_force.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/effects_of_current/lorentz_force.htm


12/18

12

For the case where Magnetic Field B is

always directed along the tangent to perimeter of a closed curve, and

constant in magnitude all along the perimeter with a value B, the Amperecircuital

laws states:

B x (perimeter of closed circuit) = o x ( Total current passing through any

surface of which the closed circuit is the

perimeter)


13/18

13

Forces acting on charges moving in magnetic andelectric fieldsare used todeflect and focus beams of electrons in many practical devices. Perhaps the most

common (but rather complicated) example of this is the TV tube. The image onthe face of the tube is due to a beam of electrons hitting a coating of a materialcalled phosphor which emits light on being struck. The beam of electrons isdeflected in a very complex way be electric fields applied to parallel platesbetween which the beam passes.

The medium around a charge is always under stress and that a force acts on apositive or negative charge when placed in that medium this reason in which stressexists is called an electric field. It is also known as a dielectric field or electrostaticfield.

Astatic chargeproduce a radial electric field that aligns grass seeds to show thefield direction. We usually represent the field with the thin solid lines (witharrows) that we call lines of force.
http://www.ncert.nic.in/html/learning_basket/electricity/electricity/charges%20&%20fields/electric_field.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/charges%20&%20fields/electric_field.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/charges%20&%20fields/electric_field.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/electrostatics/static_electricity.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/electrostatics/static_electricity.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/electrostatics/static_electricity.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/electrostatics/static_electricity.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/charges%20&%20fields/electric_field.htm


14/18

14


15/18

15

Mathematically, it is expressed as :

Q1Q2

F --------

d2

Q1Q2

or F =K--------

d

2

In S.I. and M.K.S. system, k = 1/4po. Hence the above equation becomes,

Q1Q2

F = ----------

4pod2

Now,

1 1-------- = ------------- = 8.9878 x 109 = 9 x 109 (approx.)4 4 x 8.854 x 10-12
http://www.ncert.nic.in/html/learning_basket/electricity/charges%20&%20fields/coulomb.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/charges%20&%20fields/coulomb.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/charges%20&%20fields/coulomb.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/charges%20&%20fields/coulomb.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/charges%20&%20fields/coulomb.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/charges%20&%20fields/coulomb.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/charges%20&%20fields/coulomb.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/charges%20&%20fields/coulomb.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/charges%20&%20fields/coulomb.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/charges%20&%20fields/coulomb.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/charges%20&%20fields/coulomb.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/charges%20&%20fields/coulomb.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/charges%20&%20fields/coulomb.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/charges%20&%20fields/coulomb.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/charges%20&%20fields/coulomb.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/charges%20&%20fields/coulomb.htm


16/18

16

The torque on a current loop in a uniform magnetic field is used to measureelectrical magnetic field is used to measure electrical currents. This currentmeasuring device is called amoving coilgalvanometer.

Thegalvanometerconsists of a coil of wire often rectangular, carrying thecurrent to be measured. There are generally many turns in the coil to increase itssensitivity. The coil is placed in a magnetic field such that the lines of B remainnearly parallel to the plane of wire as it turns. This is achieved by having a softiron cylinder placed at the center of the coil. Magnetic field lines tend to passthrough the iron cylinder, producing the field configuration. The moving coil ishung from a spring which winds up as the coil rotates; this winding up produces arestoring torque proportional to the winding up (or twisting) of the spring, i.e. tothe angular deflection of the coil. The coil comes to equilibrium when thisrestoring torque k balances the torque due to the magnetic field balances thetorque due to the magnetic field. Since by design field lines are radial,

we have sin q ~ 1, so that for equilibrium
http://www.ncert.nic.in/html/learning_basket/electricity/electricity/electricity/electricity/effects_of_current/galvanometer.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/electricity/electricity/effects_of_current/galvanometer.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/electricity/electricity/effects_of_current/galvanometer.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/electricity/electricity/effects_of_current/galvanometer.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/electricity/electricity/effects_of_current/galvanometer.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/electricity/electricity/effects_of_current/galvanometer.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/electricity/electricity/effects_of_current/galvanometer.htmhttp://www.ncert.nic.in/html/learning_basket/electricity/electricity/electricity/electricity/effects_of_current/galvanometer.htm


17/18

17

k = INBA

NBA = ------ I

kThus the deflection of the galvanometer is proportional to the electric

current I passing through it.


18/18

18

INTRODUCTION

Magnetic Effect of Current

In 1800s scientist Hans Oersted observe that, current flowing in a circuit effects the direction ofneedles of the compass. Picture, given below, shows his experiment. When the switch is closedcurrent passes the circuit and direction of the magnet changes under the effect of magnetic fieldproduced by current

Moreover, Faraday and Joseph Henry are other scientists showing the relation ofmagnetic field and current. If you move the magnet placed near the circuit youproduce current or, if you change the current of circuit you can get current in another

circuit placed near it. We will learn all the types of current produced by magneticfield.

Magnetic Field around a WireCurrent flowing in a linear wire produces magnetic field B=2k.i/d at a distance d.Here current measured in Ampere, distance measured in meter and k=10 -7 N/Amps.Direction of the magnetic field produced around the wire is always tangential to thecircle around the wire.

swati on magnetic effect of current

Documents

Transcript of swati on magnetic effect of current