Question

A current loop, carrying a current of 6.8 A, is in the shape of a right triangle with sides 30, 40, and 50 cm. The loop is in a uniform magnetic field of magnitude 77 mT whose direction is parallel to the current in the 50 cm side of the loop. Find the magnitude of (a) the magnetic dipole moment of the loop in amperes-square meters and (b) the torque on the loop.

Answer 1

(a)
`0.408\ Am^(2)`

(b) 0.03142 Nm

Solution:

As per the question:

Current, I = 6.8 A

Magnetic field, B = 77 mT = 0.077 T

Now,

Area of the loop, A =
`(1)/(2)* base* height`

A =
`(1)/(2)* 0.3* 0.4 = 0.06\ m^(2)`

(a) To calculate the magnetic dipole moment in the loop:

`\mu = I* A`

where

`\mu` = Magnetic dipole moment

`\mu = 6.8* 0.06 = 0.408\ Am^(2)`

Now,

(b) To calculate the torque in the loop:

`\tau = \mu B = 0.408* 0.077 = 0.03142\ Nm`