A particle of charge q moves in a circle of radius a with speed v. Treat the circular path as a current loop with a constant current equal to the ratio of the particles charge magnitude to its period of motion. Find the maximum possible magnitude of the torque produced on the loop by a uniform magnetic field of magnitude B. (Use any variable or symbol stated above as necessary. Assume all quantities are in SI units.)

The magnitude is 6.87 * 10^-26N.m

Explanation:

There are missing details in this question.

To solve this question, I'll assume the values of radius, speed and the magnitude of magnetic speed.

Let r = radius = 5.3 * 10^-11m

Let v = speed = 2.2 * 10^6 m/s

Magnitude = 7.0mT

First, we'll calculate the period of the motion..

This is calculated using 2πr/v

T = 2 * π * 5.3 * 10^-11/2.2 * 10^6

T = 1.513676460365E−16

I = 1.514 * 10^-16

Then we calculate the current.

Current, I = e/T where T = 1.69 * 10^-19

So I = 1.69 * 10^-19/1.514 * 10^-16

I = 0.001116248348745

I = 0.001112 A

Next we calculate area

Area = πr²

Area = π(5.3 * 10^-11)²

Area = 8.824733763933E−21

Area = 8.825E-21 m²

Lastly, the maximum magnitude produced by the torque is calculated as:.

i * Area * Magnitude

0.001112 * 8.825 * 10^-21 * 7 * 10^-3

6.86938E−26.

Hence, the magnitude is 6.87 * 10^-26N.m

the minimum amperage that the current in this wire would have to have so that its weight is completely supported by the magnetic force due to earth's field, assuming that no other forces except gravity act on it

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