A square loop of wire with a small resistance is moved with constant speed from

Question

A square loop of wire with a small resistance is moved with constant speed from a field free region into a region of uniform B field (B is constant in time) and then back into a field free region to the right. The self inductance of the loop is negligible.

True False  When leaving the field the coil experiences a magnetic force to the right.
True False  Upon leaving the field, a counterclockwise current flows in the loop.
True False  When entering the field the coil experiences a magnetic force to the right.
True False  Upon entering the field, a counterclockwise current flows in the loop.

Explanation / Answer

(a) True

When inside the field, then magnetic flux through the coil is out of plane of figure. When leaving the field, the flux decreases. This means that change in flux is into the plane of figure.
Therefore, the current in the loop is such that the flux produced by it is out of the plane of figure. For that the magnetic field produced by the current should be out of the plane of figure. This is possible when the current is anticlockwise.

(b) False.

Apply Gauss's law, the current is clockwise.

(c) True

Current directions in the top and the bottom sides of the loop are in opposite directions. Both are in the same magnetic field. Therefore, forces on them are equal and opposite and cancel each other. The right side of the loop is outside the magnetic field and, therefore, experiences no magnetic force.
So, the net force on the loop is the force on the left side. The current in the loop is clockwise. For this, the current in the left side is from bottom to top.
And magnetic field is out of the plane of figure. The direction of force is in the direction of cross product of direction of current and direction of field. This direction is towards right.

(d) True

Before entering the field, the magnetic flux through the coil is zero. Upon entering the field, the flux is out of the plane of figure because magnetic field is out of the plane of figure. So, the change in flux is out of the plane.

Therefore, the current in the loop is such that the flux produced by it is into the plane of figure. For that the magnetic field produced by the current should be into the plane of figure. This is possible when the current is conterclockwise.

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