Question

A circular coil of 234 turns has a radius of 1.96 cm. (a) Calculate the current that results in a magnetic dipole moment of magnitude 2.57 A·m2. (b) Find the maximum magnitude of the torque that the coil, carrying this current, can experience in a uniform 42.7 mT magnetic field.

Answer 1

Answer:

a) $I = 9.1785 A$

b) τ = 0.109 N m (max)

Explanation:

given

magnetic dipole moment   μ = 2.57 Am²

number of turns N = 234

            radius r     = 1.96 cm  = 0.0196 m

using μ  = N I A  

where I is current  and A is area

I = μ/NA

 $I= \frac{2.57}{234 \times\pi r^2}$

$I= \frac{2.57}{234 \times\ 3.14 \times(0.0196) ^2}$

$I = \frac{2.57}{0.28}$

$I = 9.1785 A$

for max torque

we know τ = μΒ

τ  =  2.57 ×0.0427

τ = 0.109 N m (max)