Friday, February 8, 2008

IIT JEE Physics Formula Revision 34. Magnetic Field

1. Magnetic field can be defined mathematically as

F = qv × B

Equation uniquely determines the direction of magnetic field B from the rules of the vector product.

F = force (vector)
q = charge
v = velocity (vector)
B = magnetic field (vector)

2. Motion of a Charged particle in a uniform magnetic field

qvB = mv²/r

r = mv/qB

The time taken to complete the circle is
T = 2πr/v = 2πm/qB

Frequency of revolutions is

ν = 1/T = qB/2πm
This frequency is called cyclotron frequency.

6. If a straight wire of length l carry8ng a current i is placed in a uniform magnetic field B, the force on it is

F = il×B

i = current in the conductor
l = vector of length of the conductor
B = magnetic field

7. Formula for Torque on a current loop

If there is a rectangular loop carrying current i in a uniform magnetic field B
then net torque acting on the loop is

Г = iABsin θ

Where i = current in the loop
A = area (magnitude)
B = magnetic field (magnitude)
θ = the angle of inclination of the loop with the plane perpendicular to the plane of magnetic field.

We can also define in terms of vector

Г = iA× B

iA can be termed as μ the magnetic dipole moment or simply magnetic moment of the current loop.

If there are n turns in the loop, each turn experiences a torque.

The net torque is
Г = niA× B

μ = niA

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