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Question #43394

Difficulty: 8/10 | 🟢 Free

The Question

Consider a semi-infinite block of highly permeable magnetic material (relative permeability $\mu_r \to \infty$ ) occupying the region $x \ge 0$ . An infinitely long straight wire carrying a steady current $I$ in the $+\hat{z}$ direction is placed in the vacuum region ( $x < 0$ ) at $x = -d, y = 0$ . Find the magnitude of the magnetic field $\vec{B}$ at the point $P$ located at $x = -d, y = d$ .

Options

A.
$\frac{\sqrt{10}\mu_0 I}{5\pi d}$
B.
$\frac{\mu_0 I}{2\pi d}$
C.
$\frac{\sqrt{5}\mu_0 I}{5\pi d}$
D.
$\frac{3\mu_0 I}{5\pi d}$

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

Ampere’s Circuital Law Symmetry|Principle of Superposition|Integration (Path Integral)

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to recognize the breakdown of standard Amperean azimuthal symmetry near a high-permeability boundary.

Students commonly fall into the trap of either ignoring the boundary entirely (yielding the standard vacuum field, Option B) or incorrectly applying the electrostatic method of images by reversing the sign of the image current (analogous to a positive charge near a grounded conductor, yielding Option C).

In magnetostatics, the boundary condition for $\mu_r \to \infty$ requires the tangential $\vec{H}$ field to vanish, which necessitates an image current in the same direction as the source current, fundamentally altering the superposition of the magnetic field vectors.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Moving Charges and Magnetism - Class 12
Concept	Ampere’s Circuital Law Symmetry
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free