Question

Given, B = magnetic induction and R = radius of the path, the energy of a charged particle coming out of a cyclotron is given by ______.

Options

• `(qB^2R^2)/(2m)`

• `(q^2BR^2)/(2m)`

• `(q^2BR)/(2m)`

• `(q^2B^2R^2)/(2m)`

Answer 1

Given, B = magnetic induction and R = radius of the path, the energy of a charged particle coming out of a cyclotron is given by `bbunderline((q^2B^2R^2)/(2m)`).

Explanation:

Given: B = magnetic induction

R = radius of the path, 

Formula: R = `(mv)/(qB)`

mv = RqB

Thus kinetic energy,

K = `1/2  mv^2`

= `(RqB)^2/(2m)`

= `(q^2B^2R^2)/(2m)`