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Question #43405

Difficulty: 8/10 | 🟢 Free

The Question

Two identical circular loops, each of radius $R$ , are placed coaxially along the $z$ -axis with their centers at $z = R/2$ and $z = -R/2$ . The loops carry equal currents $I$ in opposite directions. A small magnetic dipole of mass $M$ and magnetic dipole moment $\vec{p} = p_0 \hat{k}$ is released from rest at the origin $(0,0,0)$ . Neglecting gravity, what is the magnitude of the initial acceleration of the dipole?

Options

A.
0
B.
$\frac{24 \mu_0 p_0 I}{25\sqrt{5} M R^2}$
C.
$\frac{48 \mu_0 p_0 I}{25\sqrt{5} M R^2}$
D.
$\frac{16 \mu_0 p_0 I}{25\sqrt{5} M R^2}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Magnetic Field on Axis vs. Center|Neutral Equilibrium Points|Vector Cross-Products

Why This Question Is Tricky

Common Mistakes

This question tests the critical distinction between a zero magnetic field and a zero magnetic field gradient.

Students often fall into the trap of assuming that because the net magnetic field at the midpoint of the two opposing loops is zero ( $B=0$ ), a magnetic dipole placed there will experience no force and remain in equilibrium.

However, the force on a magnetic dipole is determined by the gradient of the field ( $F = \nabla(\vec{p} \cdot \vec{B})$ ), not the field itself.

By setting the currents in opposite directions, the setup creates a steep field gradient at the origin, resulting in a non-zero net force and subsequent acceleration.

This highlights the danger of conflating field strength with field gradient in dipole interactions.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Moving Charges and Magnetism - Class 12
Concept	Magnetic Field on Axis vs. Center
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free