Question

Find out the polarity of the capacitor in the following figure: -

Answer 1

Hint: We will first apply Lenz law to find out the direction of the induced magnetic field in the wire loop and then apply Right Hand Thumb’s rule to find the direction of the induced current. Finally, we will determine the polarity of the capacitor using the direction of current flow in the wire loop.

Complete Answer: We will first understand the orientation of the capacitor, wire loop, and bar magnet in the above circuit. The capacitor and the bar magnet are in the plane of the paper and the wire loop is perpendicular to the plane of the paper in the above figure.
Now, we know that magnetic field lines outside the bar magnet originate at the south pole and end at the north pole. Thus, we see that magnetic field lines are going inside the loop from right to left direction in the current case. So, this means that the bar magnet will cause the magnetic field to have a direction from right to left inside the wire loop. This magnetic field is marked as B in the diagram.
Now, we will apply Lenz law to find the direction of the induced magnetic field in the wire loop: -
Lenz Law: According to Lenz law the induced magnetic field in a loop of wire will oppose a change in magnetic flux through the loop.
To oppose the change in flux, a magnetic field will be induced in a direction opposite to that caused by the bar magnet. Thus, we have an induced magnetic field in the direction left to right. This induced magnetic field is marked as B’ in the diagram.
Now, we will apply the right-hand thumb rule to find the direction of induced current in the wire loop: -
Right-Hand Thumb Rule: If a current-carrying conductor is imagined to be held in the right hand such that thumb points in the direction of current then curled fingers of hand indicate the direction of the magnetic field.
To induce a magnetic field in the left to the right direction, the current has to pass in the loop from a to b direction.

If current flows from a to b, a positive charge will be accumulated on plate ‘b’ and the equal and opposite negative charge will be accumulated on plate ‘b’ of the capacitor.

Thus, the polarity of the capacitor becomes: -
A plate = negative terminal
B plate = positive terminal

Note: There is a shortcut alternate method for doing such questions. The side of the wire loop facing the bar magnet will try to repel the bar magnet and form a pole opposite to the pole of the bar magnet facing towards it. In this case, the wire loop will form a north pole as the south pole side of the bar magnet is facing towards it.

Now, to form a north pole the current must flow in the anticlockwise direction, that is, from a to b. Thus, the polarity of the capacitor becomes:
A plate = negative terminal
B plate = positive terminal