Three identical closed coils A, B and C are placed with their planes parallel to one another. Coils

Q: Why doesn't coil C induce any current in coil B?

Coil $C$ is stationary and carries a constant current. Therefore, the magnetic flux it produces through coil $B$ is constant. Since electromagnetic induction requires a *change* in flux, coil $C$ does not induce any current.

Q: What would happen if coil A was moving away from coil B?

If coil $A$ was moving away, the leftward magnetic flux through $B$ would decrease. To oppose this decrease, coil $B$ would produce a leftward magnetic field, meaning the induced current would be in the *same* direction as coil $A$.

Q: How do we use the right-hand rule here?

Curl the fingers of your right hand in the direction of the current in the coil. Your extended thumb will point in the direction of the magnetic field inside the coil.

Q: Does the speed of coil A affect the direction of the induced current?

No, the speed of coil $A$ only affects the *magnitude* of the induced current (faster motion = greater rate of change of flux = larger current). The *direction* is determined solely by whether the flux is increasing or decreasing.

Q: What if coil B was also moving at the same velocity as coil A?

If both coils move at the same velocity, their relative distance remains constant. The magnetic flux through $B$ would not change, and therefore, no current would be induced in $B$.

Question

Three identical closed coils $A$, $B$ and $C$ are placed with their planes parallel to one another. Coils $A$ and $C$ carry equal currents as shown in figure. Coils $B$ and $C$ are fixed in position and coil $A$ is moved towards $B$ with uniform motion. Is there any induced current in $B$ ? If no, give reasons. If yes, mark the direction of the induced current in the diagram.

Sigma Percentile · Accepted Answer

### The Setup: A Tale of Three Coils

Imagine you are standing on the central axis looking at three parallel coils: $A$, $B$, and $C$. Coils $A$ and $C$ are actively carrying steady currents, while coil $B$ sits quietly in the middle, completely neutral with no initial current.

The twist in our story begins when coil $A$ starts moving towards coil $B$ with a uniform velocity $v$. Our goal is to determine if this motion awakens coil $B$ by inducing a current, and if so, in what direction.

### The Magnetic Field of Coil A

Before we analyze the motion, we must understand the magnetic environment created by coil $A$. By observing the current arrow on coil $A$, we can use the **Right-Hand Grip Rule**. If you curl the fingers of your right hand in the direction of the current flowing through coil $A$, your extended thumb points in the direction of the magnetic field it produces.

Applying this rule, we find that the magnetic field $B_A$ generated by coil $A$ points from **right to left**.

### The Approach: Changing Flux

As coil $A$ moves closer to coil $B$, it brings its magnetic field along with it. The magnetic field lines passing through coil $B$ become increasingly denser. In physics terms, the leftward magnetic flux $\Phi_B$ passing through the area of coil $B$ is **increasing**.

According to Faraday's Law of Electromagnetic Induction, a changing magnetic flux through a closed loop induces an electromotive force (EMF), which in turn drives an induced current.

### Lenz's Law: The Resistance

Nature loves equilibrium, and **Lenz's Law** is the ultimate enforcer of this rule. It states that an induced current will always flow in a direction that opposes the change in magnetic flux that produced it.

Since the leftward magnetic flux through coil $B$ is increasing, coil $B$ will fight back. To oppose this increase, coil $B$ must generate its own magnetic field $B_{	ext{ind}}$ pointing in the opposite direction—from **left to right**.

### The Final Verdict

Now, we reverse-engineer the Right-Hand Grip Rule for coil $B$. To produce a rightward magnetic field, the induced current $I_{	ext{ind}}$ in coil $B$ must flow in the exact opposite direction to the current in coil $A$.

But wait, what about coil $C$? Coil $C$ is stationary and carries a constant current. Because it isn't moving and its current isn't changing, the magnetic flux it contributes to coil $B$ remains perfectly constant ($\frac{d\Phi_C}{dt} = 0$). Therefore, coil $C$ plays absolutely no role in inducing any current in coil $B$.

Thus, the final answer is **Yes, a current is induced in coil $B$, and it flows in the direction opposite to the current in coil $A$.**

Visualized Solution

$I ni t ia l S e t u p$

$M a g n e t i c F i e l d o f C o i l A$

$C han g e in M a g n e t i c F l ux$

$L e n z^{'} s L a w$

$D i r ec t i o n o f I n d u ce d C u r r e n t$

$R o l e o f C o i l C$

The Sigma Insight: Lenz's Law

The Setup

The Magnetic Field of Coil A

The Approach

Lenz's Law

The Final Verdict

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