Respuesta :
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 = [tex]\frac{mv}{qr}[/tex]
Here, m = mass of proton = [tex]1.67 \times 10^{-27}[/tex] kg
v = velocity = 10% of [tex]3 \times 10^{8}[/tex] = [tex]3 \times 10^{7}[/tex] m/s
q = charge of proton = [tex]1.6 \times 10^{-19} C[/tex]
r = radius = [tex]\frac{60}{2}[/tex] = 30 cm = 0.30 m (as 1 m = 100 cm)
Therefore, magnetic field will be calculated as follows.
B = [tex]\frac{mv}{qr}[/tex]
= [tex]\frac{1.67 \times 10^{-27} \times 3 \times 10^{7}}{1.6 \times 10^{-19} C \times 0.30 m}[/tex]
= [tex]\frac{5.01 \times 10^{-20}}{0.48 \times 10^{-19}}[/tex]
= 1.0437 T
Thus, we can conclude that magnetic field strength is 1.0437 T.
