While the resistance of the variable resistor in the left-hand solenoid is decreased at a constant rate, the induced current through the resistor RRR will

The induced current through resistor R will

b) flow from a to b

Explanation:

The image is shown below, and the full question is written down as

The two solenoids in the figure are coaxial and fairly close to each other. While the resistance of the variable resistor in the left-hand solenoid is decreased at a constant rate, the induced current through the resistor R will

a) Flow from b to a

b) flow from a to b

c) be zero because the rate is constant.

From the image, the current in the left hand solenoid flows from the positive terminal of the battery to the negative terminal in an anticlockwise direction by convention.

Varying a rheostat causes a change in the resistance of electricity through the solenoid, and a changing current through a solenoid will induce current to flow through another solenoid placed nearby. Therefore, the left-hand solenoid induces a current flow on the right-hand solenoid.

Since the current in the left-hand solenoid flows in an anticlockwise direction, then it will have an equivalent magnetic polarity of a north pole on a magnet.

Also remember that Lenz law states that the induce current acts in such a way as to oppose the motion, or action producing it.

In this case, the induced current in the right-hand solenoid will act as to repel the left-hand solenoid away from itself. The only way is by the right-hand solenoid also having a north pole equivalent magnetic pole on it since like poles repel each other. This means that the induced current in the right-hand solenoid will flow in an anticlockwise manner too, from a to b.