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 60 cm in diameter.

Answer 1

The given question is incomplete. The complete question is as follows.

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 60 cm in diameter.

What magnetic field strength will you need?

Explanation:

Formula for the strength of magnetic field is as follows.

      B = $\frac{mv}{qr}$

Here,    m = mass of proton = $1.67 \times 10^{-27}$ kg

      v = velocity = 10% of $3 \times 10^{8}$ = $3 \times 10^{7}$ m/s

      q = charge of proton = $1.6 \times 10^{-19} C$

      r = radius = $\frac{60}{2}$ = 30 cm = 0.30 m   (as 1 m = 100 cm)

Therefore, magnetic field will be calculated as follows.

            B = $\frac{mv}{qr}$

               = $\frac{1.67 \times 10^{-27} \times 3 \times 10^{7}}{1.6 \times 10^{-19} C \times 0.30 m}$

               = $\frac{5.01 \times 10^{-20}}{0.48 \times 10^{-19}}$

               = 1.0437 T

Thus, we can conclude that magnetic field strength is 1.0437 T.