Two concentric circular conducting loops, P and Q, lie flat in the same horizontal plane, … — JAMB UTME

Two concentric circular conducting loops, $P$ and $Q$ , lie flat in the same horizontal plane, with loop $Q$ situated inside loop $P$ . Loop $P$ is connected to a DC power source through a variable resistor and initially carries a steady clockwise current. If the resistance of the variable resistor is suddenly decreased, which of the following correctly describes the direction of the induced current in loop $Q$ and the nature of the magnetic force exerted on loop $Q$ ?

The induced current in $Q$ is counter-clockwise, and the magnetic force on $Q$ is repulsive.Answer
B
The induced current in $Q$ is clockwise, and the magnetic force on $Q$ is attractive.
C
The induced current in $Q$ is counter-clockwise, and the magnetic force on $Q$ is attractive.
D
The induced current in $Q$ is clockwise, and the magnetic force on $Q$ is repulsive.

Answer

The induced current in loop

Q

flows in a counter-clockwise direction, and the magnetic force between loop

P

and loop

Q

is repulsive.

Decreasing the variable resistance increases the clockwise current in loop

P

, which increases the downward magnetic flux through loop

Q

. By Lenz's law, loop

Q

generates an opposing upward magnetic flux, which corresponds to a counter-clockwise induced current. Because the two loops carry currents flowing in opposite directions, they exert a repulsive magnetic force on each other.

Step-by-Step Solution

Determine the initial magnetic field direction created by loop

P

Using the right-hand grip rule, a clockwise current in outer loop

P

produces a magnetic field directed perpendicularly downward (into the plane of the page) inside the loop.

Current in a circular loop generates an axial magnetic field whose direction is given by the right-hand rule.

Analyze the change in magnetic flux through inner loop

Q

Decreasing the resistance increases the current in loop

P

, thereby increasing the downward magnetic flux passing through loop

Q

Ohm's law (

I = V/R

) indicates that reducing resistance increases current, which proportionally strengthens the magnetic field (

B \propto I

Apply Faraday's and Lenz's laws to find the induced current direction in

Q

To oppose the increasing downward flux, the induced current in loop

Q

must produce a magnetic field directed upward (out of the page). By the right-hand grip rule, an upward field requires a counter-clockwise current in loop

Q

Lenz's law states that an induced current always flows in such a direction that its magnetic effect opposes the change producing it.

Determine the nature of the magnetic force between the two loops

Loop

P

carries a clockwise current while loop

Q

carries a counter-clockwise current. Concentric circular conductors carrying currents in opposite directions repel each other.

Opposing electric currents produce magnetic fields that result in mutual magnetic repulsion.

Key Concept

Lenz's Law and Electromagnetic Induction in Coaxial Loops

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