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