A magnetic needle is kept in a non-uniform magnetic field. It experiences
(a) a force and a torque
(

Q: Can the net force ever be zero in a non-uniform field?

Generally, no. The only exception is if the dipole is placed symmetrically in a very specific field configuration where the field gradient is zero at the center, but practically, a non-uniform field implies a non-zero gradient, leading to a net force.

Q: What happens in a uniform magnetic field?

In a perfectly uniform magnetic field, the field strength $\mathbf{B}$ is identical everywhere. The force on the North pole exactly cancels the force on the South pole, resulting in zero net force. However, a net torque will still exist unless the needle is perfectly aligned with the field.

Q: Why does the needle experience a torque?

Torque arises because the forces on the two poles act at different points (separated by the length of the needle). Since their lines of action do not coincide, they create a rotational effect.

Q: In which direction will the net force act?

The net force generally pulls the magnetic dipole towards the region where the magnetic field is stronger, assuming the dipole is aligned with the field.

Q: Is a magnetic needle different from a current-carrying loop?

Conceptually, no. Both act as magnetic dipoles. A small current loop in a non-uniform field will also experience both a net force and a net torque, governed by the same principles.

Question

A magnetic needle is kept in a non-uniform magnetic field. It experiences

Options:

(A) a force and a torque

(B) a force but not a torque

(C) a torque but not a force

(D) neither a force nor a torque

Sigma Percentile · Accepted Answer

Imagine you are holding a tiny compass needle. This needle is nothing but a miniature bar magnet, a classic magnetic dipole with a North pole and a South pole. Now, what happens when you place this delicate needle into a magnetic field? The answer depends entirely on the **nature** of that field.

### The Uniform Illusion

Let's first consider a perfectly uniform magnetic field. In this idealized scenario, the magnetic field lines are perfectly parallel and equally spaced, meaning the magnetic field strength and direction are identical everywhere.

When our magnetic needle is placed here, the North pole experiences a force pulling it in the direction of the field, given by $\mathbf{F}_N = m\mathbf{B}$. Simultaneously, the South pole experiences an exact opposite force, $\mathbf{F}_S = -m\mathbf{B}$. Because the field $\mathbf{B}$ is exactly the same at both poles, these two forces are equal in magnitude and opposite in direction.

What is the result? The net translational force is exactly zero ($\mathbf{F}_{net} = 0$). The needle won't be pulled left or right. However, unless the needle is perfectly aligned with the field lines, these forces act at different points, creating a couple. This results in a **net torque** ($\boldsymbol{	au}_{net} 
eq 0$), which simply spins the needle until it aligns with the field.

### The Non-Uniform Reality

But the real world is rarely perfectly uniform. Our problem places the needle in a **non-uniform magnetic field**. Here, the magnetic field lines might converge, diverge, or curve, meaning the field strength $\mathbf{B}$ changes from point to point.

Now, let's look at the forces again. The North pole is at a specific location experiencing a local field $\mathbf{B}_N$, so the force is $\mathbf{F}_N = m\mathbf{B}_N$. The South pole is at a different location experiencing a different local field $\mathbf{B}_S$, so its force is $\mathbf{F}_S = -m\mathbf{B}_S$.

Here is the crucial catch: Because the field is non-uniform, **$\mathbf{B}_N$ is not equal to $\mathbf{B}_S$**.

### The Inevitable Result: Force and Torque

Since the magnetic field strengths at the two poles are different, the forces acting on them are unequal in magnitude and potentially slightly different in direction.

When you add these two unequal vectors together, they do not cancel out. 
$$ \mathbf{F}_{net} = \mathbf{F}_N + \mathbf{F}_S 
eq 0 $$
This means the needle experiences a **net force**. It will physically accelerate and translate through space, typically being pulled towards the region where the magnetic field is strongest.

Furthermore, just like in the uniform case, these forces are acting at different points along the needle. Because their lines of action do not perfectly coincide and cancel, they create a turning effect.
$$ \boldsymbol{	au}_{net} = \mathbf{r}_N 	imes \mathbf{F}_N + \mathbf{r}_S 	imes \mathbf{F}_S 
eq 0 $$
This means the needle also experiences a **net torque**, causing it to rotate.

In conclusion, a magnetic needle in a non-uniform magnetic field is subjected to a beautiful, complex dance: it is simultaneously twisted by a torque to align with the field and pulled by a net force toward the strongest part of the field. Therefore, it experiences both a force and a torque!

Animated Solution for Physics - Magnetic Effects of Current: A magnetic needle is kept in a non-uniform magnetic field. It experiences

Select Answer:

Visualized Solution

$Non-Uniform Magnetic Field$

$Magnetic Needle as a Dipole$

$Forces on the Poles$

$Net Force and Torque$

$Conclusion$

The Sigma Insight: Bar Magnet

The Uniform Illusion

The Non-Uniform Reality

The Inevitable Result

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