Answer the question above and clearly show the process of solving the problem. I

Question

Answer the question above and clearly show the process of solving the problem. I need to be able to understand the process of solving the problem.

The answer is given as: (picture below).

A proton moves in a circular path of radius 10-10 m with a speed of 4 times 105 m/s. Determine the magnetic moment of the current, loop, and sketch the current loop and indicate the direction of the magnetic moment(use the right hand rule). Find the magnitude of the torque exerted on the current loop if it is placed in a magnetic field of 0.2 T directed perpendicular to its magnetic moment vector. 3.2 times 10-24 A.m2. This is similar to Figure 32.21 in chapter 32 of the textbook. 6.4 times 10-25N.m

Explanation / Answer

a)

current is:

i = dq/dt

we know that at time T, a charge of "e" passes:

T = (2 pi R)/v

i = dq/dt = e/((2 pi R)/v) = e v/(2 pi R)

we have:

magnetic moment = current x area

==> m = i A

==> m = (e v/(2 pi R)) (pi R^2)

==> m = e v R/2 = (1.6e-19 * 4e5 * 1e-10)/2 = 3.2 x 10^-24 A.m2

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c)

torque = m B sin(theta) = (3.2e-24) * (0.2) * sin(90) = 6.4 x 10^-25 N.m

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