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Question #43281

Difficulty: 8/10 | 🟢 Free

The Question

An infinite composite structure consists of alternating planar sheets of a ferromagnetic material (thickness $d_1 = 3 \text{ mm}$ ) and a non-magnetic insulator (thickness $d_2 = 2 \text{ mm}$ ). The structure is placed inside a long solenoid carrying a slowly varying alternating current, which generates a nominal macroscopic external magnetic field intensity $H_{\text{ext}} = nI$ perpendicular to the sheets. The uniform magnetic induction $B$ inside the structure is measured, and a hysteresis loop of $B$ versus $H_{\text{ext}}$ is plotted for one complete cycle. If the area of this apparent hysteresis loop is $A_{\text{app}} = 150 \text{ J/m}^3$ , what is the actual energy dissipated as heat per unit volume of the ferromagnetic material per cycle?

Options

A.
$250 \text{ J/m}^3$
B.
$150 \text{ J/m}^3$
C.
$90 \text{ J/m}^3$
D.
$375 \text{ J/m}^3$

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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

Hysteresis Loop Area|Magnetic Field Line Behavior in Matter|Field due to Infinite Sheet

Why This Question Is Tricky

Common Mistakes

This question tests the understanding of magnetic boundary conditions and the distinction between macroscopic applied fields and local fields in composite media.

Students often fall into the trap of assuming the measured $B$ - $H_{\text{ext}}$ hysteresis loop area directly gives the intrinsic dissipation of the magnetic material ( $150 \text{ J/m}^3$ ).

Because $B$ is uniform (perpendicular configuration), they incorrectly assume no volume fraction correction is needed, ignoring the discontinuity in $H$ and the demagnetizing field effect.

The apparent loop area actually represents the energy dissipated per unit volume of the entire stack, requiring a volume fraction scaling to find the dissipation within the ferromagnetic sheets alone.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Magnetism and Matter - Class 12
Concept	Hysteresis Loop Area
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free