Question

A particle of charge q, mass m and velocity v moves in a circular path inside the dees of a cyclotron. If the magnetic field exerted on the particle is B, calculate the radius R of the particles path.

• A. $\frac{qvB}{m}$
• B. $\frac{qv}{m}$
• C. $\frac{mv}{qB}$
• D. $\frac{Bv}{qm}$

Answer 1

The correct option is C $\frac{mv}{qB}$

Answer is C
Centripetal force is balanced by magnetic force
The centripetal force acting on the charged particle is $\frac{m{v}^2}{R}$. Here $R$ is the path radius.
The magnetic force acting on the charged particle equals $qvB$. Note that the angle between the velocity and magnetic field is ${90}^o$.
On equating the two values we obtain $R=\frac{mv}{qB}$