Examine the figure below. A current loop is situated such that a uniform magneti

Question

Examine the figure below. A current loop is situated such that a uniform magnetic field is perpendicular to the plane of the current loop. The loop is constructed such that it can rotate about axis shown as a dashed line. The dashed line is placed halfway through one axis of the loop. Prove that torque on the loop about the dashed line is zero. Prove that the net force on the loop due to the magnetic field is zero. Would your answers to a or b change if the magnetic field was non-uniform. (Non-uniform means that the field may vary in direction or magnitude from point to point in space.) Explain. Would the net force due to the magnetic field on the loop still be zero if the angle between the magnetic field and the plane of the loop were not at right angles? Explain

Explanation / Answer

(a) & (b)
Torque on the Current loop in Magnetic Field is given by, t = i*A*B*sin()
Force on the Current Carrying loop in Magnetic Field is given by, F = i*lxB

Using Right Hand Rule,
Force on the Upper Part of the Loop will Cancel the Force on the lower part of the loop.
Similarly, Force on the Left part of the loop will Cancel the Force on the Right part of the loop.

We see that the Net Force on the Loop is Zero.
As the Net Force is Zero, Therefore Net Torque on the Loop is also Zero.

(c)
Yes the Answer would change for Force , as the above scenario is valid only for Uniform Magnetic Field.
If the Field is Non Uniform, The Force on different part of the loops would be different and hence they would not cancel each other, So Net Force on the Loop would Not be Zero.
For Torque, Even we have some Force acting on the loop, Torque remains Zero reason being, All the forces acting are parallel to the Loop which would not cause any movement along the dashed line.
So Net Torque is Zero.

(d)
Yes it would remain Zero provided the Field is Uniform, Force on a closed loop in Uniform Magnetic Field will allways be Zero.

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