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

Answer:

The magnetic field is 1.16 T.  

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.  

$qvB=\frac{mv^2}{r}\\\\B =\frac{mv}{qr}\\\\B =\frac{1.67\times 10^{-27}\times 3\times 10^{7}}{1.6\times 10^{-19}\times 0.27}\\\\B =1.16 T$