Question

A cyclotron accelerates particles of mass m and charge q. The energy of particles emerging is proportional to

• A. $\frac{q^2}{m}$
• B. $\frac{q}{m^2}$
• C. $\frac{q^2}{m^2}$
• D. $q$

Answer 1

The correct option is A $\frac{q^2}{m}$

The magnetic force will provide the required centripetal force.
So, $qvB=\frac{m{v}^2}{r}\Rightarrow v=\frac{qBr}{m}$
Kinetic energy, $K=\frac{1}{2}m{v}^2=\frac{q^2{B}^2{r}^2}{2m}$
So, option (A) is correct.