Respuesta :
Answer:
The magnetic field strength, B is 1.043 T.
Explanation:
The expression for the magnetic field is as follows as;
[tex]B=\frac{mv}{qr}[/tex]
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
[tex]v=\frac{10}{100}\times3\times10^{8}ms^{-1}[/tex]
[tex]v=3\times10^{7}ms^{-1}[/tex]
[tex]r=\frac{Diameter}{2}[/tex]
[tex]r=\frac{60}{2} cm[/tex]
r=0.30 m
Calculate the magnetic field strength.
[tex]B=\frac{mv}{qr}[/tex]
Put [tex]v=3\times10^{7}ms^{-1}[/tex], [tex]m=1.67\times10^{-27}ms^{-1} kg[/tex], [tex]q=1.6\times10^{-19}C[/tex] and r=0.30 m.
[tex]B=\frac{(1.67\times10^{-27})(3\times10^{7})}{(1.6\times10^{-19})(0.30)}[/tex]
B= 1.043 T
Therefore, the magnetic field strength is 1.043 T.
