Question

For your senior project, you would like to build a cyclotron that will accelerate protons to 10% of the speed of light. The largest vacuum chamber you can find is 54 cm in diameter. What magnetic field strength will you need?

Answer 1

The magnetic field is 1.16 T.

Step-by-step explanation:

speed, v = 10% of speed of light = 3 x 10^7 m/s

diameter, d = 54 cm

radius, r = 0.27 m

charge, q = 1.6 x 10^-19 C

mass, m = 1.67 x 10^-27 kg

Let the magnetic field is B.

The centripetal force is balanced by the magnetic force.

`qvB=(mv^2)/(r)\\\\B =(mv)/(qr)\\\\B =(1.67* 10^(-27)* 3* 10^(7))/(1.6* 10^(-19)* 0.27)\\\\B =1.16 T`