Answer to Question #88920 in Electricity and Magnetism for Shivam Nishad

Question

he pole faces of a cyclotron magnet are 100 cm in diameter and the magnetic field between the pole faces is 0.60 tesla. The cyclotron is used to accelerate protons. Calculate the kinetic energy, in eV, and the speed of the protons as they emerge from the cyclotron.

Answer 1

We can writer for the motion of a proton

$$\frac {mv^2} {r}=eBv (1)$$

Using (1) we get:

$$v=\frac { eBr } {m} (2)$$

In our case, e=1.6×10^-19 C, B=0.6 T, r=0.5 m, m=1.67×10^-27 kg

We get:

v=2.87×10⁷ m/s

The kinetic energy is equal to

$$K=\frac {mv^2} {2} (3)$$

We get:

K=4.3 MeV

Answer:

2.87×10⁷ m/s

4.3 MeV