Question

A cyclotron designed to accelerate protons has a magnetic field of magnitude 0.15 T over a region of radius 7.4 m. The charge on a proton is 1.60218×10−19 C and its mass is 1.67262 × 10−27 kg. What is the cyclotron frequency? Answer in units of rad/s.

Answer 1

Step-by-step explanation:

It is given that,

Magnetic field, B = 0.15 T

Charge on a proton,
`q=1.60218* 10^(-19)\ C`

Mass of a proton,
`m=1.67262 * 10^(-27)\ kg`

The cyclotron frequency is given by :

`f=(qB)/(2\pi m)`

`f=(1.60218* 10^(-19)\ C* 0.15\ T)/(2\pi * 1.67262 * 10^(-27)\ kg)`

f = 2286785.40 Hz

or

`\omega=14368296.44\ rad/s`

`\omega=1.43* 10^7 rad/s`

Hence, this is the required solution.