An electron moves in a circle of radius r = 5.29 times 10^-11m with speed 2.19 t

Question

An electron moves in a circle of radius r = 5.29 times 10^-11m with speed 2.19 times 10^6m/s. Treat the circular path as a current loop with a constant current equal to the ratio of the electron's charge magnitude to the period of the motion. If the circle lies in a uniform magnetic field of magnitude B = 7.10 mT, what is the maximum possible magnitude of the torque produced on the loop by the field? This is problem looks at the Bohr model of a hydrogen atom where an electron orbits a single protron and what happens when this atom is placed in a magnetic field.

Explanation / Answer

here ,

r = 5.29 *10^-11 m

speed , u = 2.19 *10^6 m/s

B = 7.1 mT

Now , let the current is I

I = e/(2 pi * r/u)

I = 1.602 *10^-19/(2pi * 5.29 *10^-11/(2.19 *10^6))

I = 1.06 *10^-3 A

maximum possible magnitude of torque = I * A * magnetic field

maximum possible magnitude of torque = pi * r^2 * I * B

maximum possible magnitude of torque = pi * (5.29 *10^-11)^2 * 1.06 *10^-3 * 0.071

maximum possible magnitude of torque = 6.62 *10^-25 N.m

the maximum possible magnitude of torque is 6.62 *10^-25 N.m

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