Question

A bar magnet whose magnetic dipole moment is$<4,0,1.5>{\mathbf{\text{A.m}}}^{\mathbf{2}}$is suspended from a thread in a region where external coils apply a magnetic field of$<0.8,0,0>\mathbf{\text{T}}$. What is the vector torque that acts on the bar magnet?

Short answer

The vector torque that acts on the bar magnet is$<0,1.2,0>\text{N·m}$.

Step-by-step solution

Given Information

The dipole moment by and the magnetic field is .

Magnetic Dipole Moment

The magnetic dipole moment magnet is defined as a vector pointing in the direction of the magnetic field that the loop makes along its axis. The torque provided by each of the magnetic forces around the axle is equal to the distance from the axle times the component of the force perpendicular to the lever arm.

Torque on magnet dipole is given by:

$\overrightarrow{\tau }=\overrightarrow{\mu }\times \overrightarrow{B}$

Calculate the vector torque

Substitute the given values of and into the above formula to get the vector of the torque.