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Posted on April 8, 2011 by admin

Given below is a last minute revisioner of Magnetism for the IIT JEE Physics paper . Note that the

points covered are based on the exam point of view , and is not meant to be a comprehensive

review of the entire magnetism portion.

A moving charge / flowing electric current produces a magnetic feild ( which is a vector feild

) in addition to the electric force / feild . If a charged particle movesparallel to the magnetic

feild, the magnetic force on the charge is zero . The magnetic force differs from an electric

force in the fact that a) it depends on the particle velocityb) its direction is perpendicular to

both |v| and|B| and c) it does no work in displacing a charged particle , provided the magnetic

feild is constant.

Consider a charged particle of mass m moving in an uniform magnetic feild | B | having an

initial velocity vector | v| perpendicular to the feild. Then , the path radius = r = mv/ qB ,

angular speed = qB/m and time period, T = 2 m/qB.If the motion in the uniformmagnetic feild is at some arbitrary angle with respect to B , then thepath becomes helical

here there are two velocity components, the perpendicular component moving the charge in a

circular path of radius given by r = mv1/qB and the parallel component moving along the

feild lines. Pitch p = 2 m v/qB.

Consider a charged particle moving in an electric feild which is perpendicular to the magnetic

feild . Here , the particle velocity is perpendicular to both the feilds. The magnetic feild will

rotate the particle in a circle in the x-z plane , || to the magnetic feild resulting in a helical

path with increasing pitch . vx = vo cos ( Bqt/m ) and vz = vo sin ( Bqt/m ) .

A current carrying conductor of any arbitrary shape in an uniform magnetic feild will

experience a force |F| = I|L|x|B| where |L| is the length vector joining initial and final points

of a conductor. If its a closed loop then |F| = zero. If the magnetic feild is not uniform

, various elements of the loop will experience different forces - means that if the loop is free

enough , the loop could have a circular motion , ie , |Fr| = zero, but | | may or may not be

zero.

Considering the force between two infinite , parallel current carrying conductors , the force /

unit length = o I I/2 r . Note that the if the direction of current flow is the same , the

wires will attract each other.

As the magnetic feild pattern produced by a small current loop is like a bar magnet, it acts like

a magnetic dipole . Here , if the loop is not lying in a single plane , two equal and opposite

currents are to be assumed in a single branch [ note that the net change is zero ] and likewise

the required loops are to be considered in different planes . For eg , for a cube of side I

carrying a current i , |M| net = i I ( i + k ) .

If a magnetic dipole changes its orientation in a magnetic feild by an infinitesimal angular

displacement d , the feild does work dW given by d = dU, the change in potential

energy. The energy present in the loop is U = |M| |B| .

A moving point charge with velocity v creates circular magnetic feilds centered on the line of v

and which are perpendicular to it. The magnetic feild , |B| = ( o /4 ) q|v|r/r .

For a current carrying straight wire , the feild is zero for points along the length of the wire ,

but not on it. Here , as the feild is perpendicular to the plane containing both the wire and thepoint , the lines of force are concentric circles which encircle the wire. For the infinite long

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wire , if thepoint is near the end, B = ( o /4 ) 2I/d and if thepoint is near one end,

then, B = ( o /4 ) I/d .

The magnetic feild at the centre of a current carrying arcis B = o I/2 R b) apoint inside a

long solenoidB = o n I c) for apoint at one end of a long solenoid B = o n I /2 and d)

for apoint at a distance R from the centre of a flat strip of width a along its perpendicular

bisector, B = ( o i / a ) tan - ( a/2R) Note in cases where thepoints considered are

far from the strip , B = ( o /2 ) ( i/R ) .

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