A cyclotron is designed to accelerate protons (mass 1.67 $\times$ 10^-27 kg) up to a kinetic energy of 2.5 $\times$ 10^-13 J. If the magnetic field in the cyclotron is 0.75 T,what is the radius of the dipole magnets in the cyclotron? A) 14 cm B) 24 cm C) 17 cm D) 5.8 cm

Question

Quizplus · Accepted Answer

The radius of the dipole magnets can be calculated using the formula:
r = (mv) / (qB)

where,
m = mass of proton = 1.67 x 10^-27 kg
v = velocity of proton = √(2KE/m)
KE = 2.5 x 10^-13 J
B = magnetic field strength = 0.75 T
q = charge of proton = 1.6 x 10^-19 C

Substituting the values in the formula, we get:

v = √(2KE/m) = √(2 x 2.5 x 10^-13 / 1.67 x 10^-27) = 1.73 x 10^7 m/s

r = (mv) / (qB) = (1.67 x 10^-27 x 1.73 x 10^7) / (1.6 x 10^-19 x 0.75) = 0.24 m = 24 cm

Therefore, the answer is B) 24 cm.

A Cyclotron Is Designed to Accelerate Protons (Mass 1 ×\times× 10-27 Kg) Up to a Kinetic Energy of 2

A Cyclotron Is Designed to Accelerate Protons (Mass 1 $\times$ 10^-27 Kg) Up to a Kinetic Energy of 2