One of the first cyclotrons,built by Lawrence and Livingston in the 1930's,accelerated protons circles in the space between two magnetic poles.The magnetic poles were shaped like flat disks with a diameter of 25 cm and the magnetic field between the plates was uniform and oriented perpendicular to the plates.The plates and proton trajectories were horizontal.The plates were parallel to each other and separated by 5 cm.The protons started traveling slowly in small circles at the center of the disks,and would begin making larger and larger circles,travelling faster and faster,until they left the region between the plates.When the protons left the magnetic region at the edge of the plates,they were travelling at 1.2 *10⁷ m/s.What was the magnetic field between the plates?

Question

Quizplus · Accepted Answer

The formula for the magnetic field in a cyclotron is given by B = (m*v)/(q*r), where m is the mass of the particle (in this case, a proton), v is the velocity of the particle, q is the charge of the particle, and r is the radius of the circular path. 
Initially, the protons are moving in a small circle at the center of the disk, so we can assume that their initial velocity is negligible. When they leave the magnetic region at the edge of the plates, their velocity is given as 1.2 x 10^7 m/s. We can assume that the radius of the trajectory is equal to the distance between the plates, which is 5 cm = 0.05 m. The charge of a proton is 1.6 x 10^-19 C. The mass of a proton is 1.67 x 10^-27 kg.

Plugging in the values, we get 
B = (m*v)/(q*r) = (1.67 x 10^-27 kg * 1.2 x 10^7 m/s)/(1.6 x 10^-19 C * 0.05 m) = 1.0 T

Therefore, the magnetic field between the plates is 1.0 T, which is choice C.

One of the First Cyclotrons,built by Lawrence and Livingston in the 1930's,accelerated