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. Part A What magnetic field strength will you need?

Answer 1

Answer:

The magnetic field strength, B is 1.043 T.

Explanation:

The expression for the magnetic field is as follows as;

$B=\frac{mv}{qr}$

Here, m is the mass, r is the radius, v is the speed, q is the charge and B is the magnetic field.

According to the given problem, 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.

v= 10% of the speed of the light

$v=\frac{10}{100}\times3\times10^{8}ms^{-1}$

$v=3\times10^{7}ms^{-1}$

$r=\frac{Diameter}{2}$

$r=\frac{60}{2} cm$

r=0.30 m

Calculate the magnetic field strength.

$B=\frac{mv}{qr}$

Put $v=3\times10^{7}ms^{-1}$, $m=1.67\times10^{-27}ms^{-1} kg$, $q=1.6\times10^{-19}C$ and r=0.30 m.

$B=\frac{(1.67\times10^{-27})(3\times10^{7})}{(1.6\times10^{-19})(0.30)}$

B= 1.043 T

Therefore, the magnetic field strength is 1.043 T.