A rectangular loop lies in the x-y plane as shown in the figure, with current ci

Question

A rectangular loop lies in the x-y plane as shown in the figure, with current circulating in the direction shown. This sits in a region of uniform 3.0 Tesla magnetic field, in the x-z plane and at an angle of 60 degree from the x-y plane. One particular B field line is shown in the figure to help you sec the geometry, but the magnetic field is uniform throughout the figure. The loop dimensions and amount of current arc such that they give the loop a magnetic dipole moment of i = 1.2 Am2. What is the magnitude of the torque on the loop

Explanation / Answer

magnetic moment is directed along perpendicular to the surface i,e. along z axis.

hence magnetic moment in vector notation=1.2 k

where k is unit vector along z axis (similarly i and j are unit vectors along x and y axis respectively)

magnetic field in vector notation=-3*cos 60 i + 3*sin 60 k

=-1.5 i + 2.5981 k

then as we know, torque is given as

cross product of magnetic moment and magnetic field

=cross product of 1.2 k and (-1.5 i +2.5981 k)

=1.8 j

hence magnitude is 1.8 m.N

option B is correct.

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