Animated Solution for Physics - Electromagnetic Induction: Two identical circular loops of metal wire are lying on a table without touching each other. Loop $A$ carries a current which increases with time. In response, the loop $B$

Have you ever wondered how objects can push or pull each other without any physical contact? This problem is a beautiful demonstration of electromagnetic induction and Lenz's Law in action. Let's dive into the invisible world of magnetic fields and see why these two loops behave the way they do.

Imagine two identical circular loops, $A$ and $B$, lying flat on a table. Loop $A$ has a current flowing through it. To make things concrete, let's assume this current is flowing in the clockwise direction.

According to the right-hand thumb rule, a clockwise current in loop $A$ generates a magnetic field that points into the page inside the loop, and out of the page outside the loop. Since loop $B$ is situated outside loop $A$, it is bathed in an outward-pointing magnetic field ($\odot$) produced by loop $A$.

Lenz's Law

The problem states a crucial detail: the current in loop $A$ is increasing with time. Because the current is increasing, the outward magnetic field it produces is also getting stronger. Consequently, the outward magnetic flux passing through loop $B$ is increasing.

Nature, however, loves equilibrium. Enter Lenz's Law, which states that an induced current will always flow in a direction that opposes the change in magnetic flux that caused it.

Since the outward flux through loop $B$ is increasing, loop $B$ will try to fight this change by creating its own magnetic field pointing in the opposite direction—into the page ($\otimes$).

The Force of Repulsion

To generate this inward-pointing magnetic field, the induced current in loop $B$ must flow in the clockwise direction.

Now, let's look at the adjacent sides of the two loops—the parts of the loops that are closest to each other. On the right side of loop $A$, the clockwise current is flowing downwards. On the left side of loop $B$, the clockwise induced current is flowing upwards.

We know from the magnetic force law that parallel wires carrying currents in opposite directions repel each other. Because the currents in the adjacent segments of the loops are anti-parallel, a repulsive force arises between them.

Therefore, loop $B$ is repelled by loop $A$. This elegant interplay of magnetic fields and induced currents perfectly illustrates the self-regulating nature of electromagnetism!