A coil is placed in a magnetic field B as shown below. A current is induced in the coil because B is

Q: Why does anti-clockwise current mean an outward magnetic field?

According to the Right-Hand Thumb Rule, if you curl the fingers of your right hand in the direction of the current (anti-clockwise), your thumb points outwards, indicating the direction of the magnetic field.

Q: What is Lenz's Law in simple terms?

Lenz's Law simply means 'nature abhors a change in flux'. If flux increases, the loop tries to decrease it. If flux decreases, the loop tries to increase it.

Q: Why can't the magnetic field be parallel to the plane of the coil?

If the magnetic field were parallel to the plane of the coil, the magnetic flux through the coil would be zero. A changing parallel field wouldn't induce any current because the flux would remain zero.

Q: How do we know the external field is decreasing and not increasing?

The induced field is outward. It is trying to add to the outward external field. It would only do this if the outward external field was losing strength (decreasing). If the external field were increasing, the induced field would point inwards to oppose the increase.

Q: What does the 'N' pole have to do with this?

Looking at the face of a coil, if the current is anti-clockwise, it acts like the North pole of a magnet (magnetic field lines coming out). It's just a handy mnemonic to remember the direction of the induced field.

Question

A coil is placed in a magnetic field $\mathbf{B}$ as shown below.

A current is induced in the coil because $\mathbf{B}$ is

Options:

(A) outward and decreasing with time

(B) parallel to the plane of coil and decreasing with time

(C) outward and increasing with time

(D) parallel to the plane of coil and increasing with time

Sigma Percentile · Accepted Answer

### The Setup: Visualizing the Invisible

Imagine you are looking at a simple loop of wire placed in an external magnetic field. In physics, we often represent a magnetic field coming out of the page (towards you) as a series of dots, much like the tip of an arrow approaching your eye.

In our problem, the central dot labeled $\mathbf{B}$ tells us exactly this: the external magnetic field is directed **outwards**, perpendicular to the plane of the coil. But this isn't just a static scene. The coil has an induced current flowing through it in the **anti-clockwise** direction. The golden question is: *Why* is this current flowing?

### The Right-Hand Rule: Decoding the Current

To understand the cause, we first need to understand the effect. An electric current doesn't just sit there; it creates its own magnetic field. Let's figure out the direction of this newly born, *induced* magnetic field.

Enter the **Right-Hand Thumb Rule**. If you take your right hand and curl your fingers in the direction of the induced current (anti-clockwise), your thumb will naturally point outwards, right at your face. This means the induced magnetic field ($\mathbf{B}_{	ext{ind}}$) is also directed **outwards**. In magnetic terms, the face of the coil looking at us is acting like a **North Pole**.

### Lenz's Law: The Universe's Stubbornness

Now we bring in the heavy artillery: **Lenz's Law**. This law is essentially the universe's way of being stubborn. It states that an induced current will always flow in a direction that **opposes the change** in magnetic flux that created it.

Mathematically, this is the negative sign in Faraday's Law: 
$$ \varepsilon = -\frac{d\Phi}{dt} $$

Think about what this means for our coil. The induced magnetic field is pointing outwards. It is *adding* to the original outward magnetic field. Why would it do that? According to Lenz's Law, it must be trying to fight a change. If it is trying to *increase* the outward field, it must be because the original outward field is **decreasing**!

### The Grand Conclusion

The coil is acting like a loyal friend. As the external outward magnetic field weakens and fades away, the coil induces an anti-clockwise current to generate its own outward magnetic field, desperately trying to keep the total magnetic flux constant.

Therefore, we can confidently conclude that the external magnetic field $\mathbf{B}$ is **outward and decreasing with time**.

Animated Solution for Physics - Electromagnetic Induction: A coil is placed in a magnetic field $B$ as shown below. A current is induced in the coil because $B$ is

Select Answer:

Visualized Solution

Visualizing the Setup

Direction of Induced Current $I_{ind}$

Induced Magnetic Field $B_{ind}$

Applying Lenz's Law

Concluding the Change in $B_{ext}$

Conceptual Extension

The Sigma Insight: Lenz's Law

The Setup

The Right-Hand Rule

Lenz's Law

The Grand Conclusion

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Animated Solution for Physics - Electromagnetic Induction: .math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A coil is placed in a magnetic field B as shown below. A current is induced in the coil because B is