Question

The relation between force on a moving charged particle and the period of rotation of the particle will be:
​

Answer 1

Answer:

Explanation:

When the velocity of a charged particle is perpendicular to the uniform magnetic field B, the particle moves in a plane perpendicular to B. This motion is known as cyclotron. Here magnetic force required to keep the particle moving in a circle.

So, F

B

​

=qvB=

r

mv

2

​

or r=mv/qB

The period of revolution, T=

v

2πr

​

=

qB

2πm

​

Thus, the period of revolution does not depend on velocity, v.

Answer 2

The relation between force on a moving charged particle and the period of rotation of the particle is (2πm)/(qB).

Explanation:

The force on a moving charged particle is given as:

F = qvB

Where,

q = Charge of the particle

v = Velocity of the particle

B = Magnitude of magnetic field

Now, the angular frequency of the charged particle is given as:

ω = 2πv = qB/m

The period of rotation is given as:

T = 2π/ω

On substituting the formula of angular frequency, we get,

T = 2π/(qB/m)

∴ T = (2πm)/(qB)