Question

An electron moves in a circle of radius r = 4.52 × 10-11 m with a speed 2.80 × 106 m/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 = 6.29 mT, what is the maximum possible magnitude of the torque produced on the loop by the field?

Answer 1

T= 633.51 x 10⁻²⁸ N.m

Step-by-step explanation:

Given that

r= 4.52 x 10⁻¹¹ m

v= 2.8 x 10⁶ m/s

B= 6.29 mT

We know that charge on electron Q

Q= 1.6 x 10⁻¹⁹ C

The time period t

t=2πr / v

Now by putting the values

t=(2 x π x 4.52 x 10⁻¹¹ ) / (2.80 x 10⁶)

t= 10.13 x 10⁻¹⁷ s

So current I

I = Q/t

I=(1.6 x 10⁻¹⁹)/(10.13 x 10⁻¹⁷)

I= 1.57 mA

The torque T given as

T = I A B

A= π x (4.52 x 10⁻¹¹) ² m²

A= 64.15 x 10⁻²² m²

T = I A B

T = 1.57 x 10⁻³ x 64.15 x 10⁻²² x 6.29 x 10⁻³ M.m

T= 633.51 x 10⁻²⁸ N.m