Question

When charged particle is moving perpendicular to
the field then the time period of revolution
(A) depends on speed of the particle
(B) doesn't depend on speed of the particle
(C) Time period is constant
(D) None​

Answer 1

Given:

When charged particle is moving perpendicular to the field.

To find:

Correct statement among the following:

(A) depends on speed of the particle

(B) doesn't depend on speed of the particle

(C) Time period is constant

(D) None

Calculation:

Let mass of charge be m , Velocity be v , magnetic field be B.

We know that the charge will move in a circular trajectory in a plane perpendicular to the direction of the magnetic field.

Radius of that trajectory be r ;

$\sf{ \therefore \: r = \dfrac{mv}{qB} }$

Now , time period be T ;

$\sf{ \therefore \: T = \dfrac{2\pi r}{v} }$

$\sf{ = > \: T = \dfrac{2\pi ( \frac{mv}{qB}) }{v} }$

$\boxed{ \sf{ = > \: T = \dfrac{2\pi m }{qB} }}$

$\sf{ = > \: T \propto \: {v}^{0} }$

Hence , time period of the charged particle does not depend upon the velocity of the particle.

OPTION A)