Question

A current of 16.0 mA is maintained in a single circular loop of 1.90 m circumference. A magnetic field of 0.790 T is directed parallel to the plane of the loop. (a) Calculate the magnetic moment of the loop. (b) What is the magnitude of the torque exerted by the magnetic field on the loop?

Answer 1

To solve this problem it is necessary to take into account the concepts related to the magnetic moment and the torque applied over magnetic moments.

For the case of the magnetic moment of a loop we have to,

$\mu = IA$

Where

I = Current

A = Area of the loop

Moreover the torque exerted by the magnetic field is defined as,

$\tau = IAB$

Where,

I = Current

A = Area of the loop

B = Magnetic Field

PART A) First we need to find the perimeter, then

$P = 2\pi r$

$r = \frac{P}{2\pi}$

$r = \frac{1.9}{2\pi}$

$r = 0.3025m,$

The total Area of the loop would be given as,

$A = \pi r^2$

$A = \pi 0.3025^2$

$A = 0.287m^2$

Substituting at the equation of magnetic moment we have

$\mu = (16*10^{-3})(0.287)$

$\mu = 4.58*10^{-3} A.m^2$

Therefore the magnetic moment of the loop is $4.58*10^{-3}Am^2$

PART B)  Replacing our values at the equation of torque we have that

$\tau = IAB$

$\tau = (16*10^{-3})(0.287)(0.790)$

$\tau = 3.62*10^{-3}Nm$

Therefore the torque exerted by the magnetic field is $3.62*10^{-3}Nm$