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Question #42959

Difficulty: 8/10 | 🟢 Free

The Question

A ferromagnetic core of volume $V = 2 \times 10^{-3} \text{ m}^3$ is subjected to an alternating magnetic field of frequency $f = 40 \text{ Hz}$ . The area of the hysteresis loop for the material is $A_{BH} = 816 \text{ J m}^{-3}$ per cycle. Assume eddy current losses are negligible. The entire thermal power generated due to the hysteresis loss is harnessed to continuously excite a sample of $\text{He}^+$ ions from their ground state to the first excited state. Calculate the number of $\text{He}^+$ ions excited per second.

(Given: $1 \text{ eV} = 1.6 \times 10^{-19} \text{ J}$ , Ground state energy of a Hydrogen atom $E_1 = -13.6 \text{ eV}$ )

Options

A.
$1.0 \times 10^{19}$
B.
$2.5 \times 10^{17}$
C.
$4.0 \times 10^{19}$
D.
$1.0 \times 10^{18}$

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

Hysteresis Loop Area|Mass Defect vs. Binding Energy|Spectral Series Limits

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to bridge macroscopic electromagnetic energy dissipation with microscopic quantum transitions.

The primary trap lies in the dimensionality of energy flux versus total energy.

Students frequently mistake the instantaneous work done on the magnetic dipoles (Energy = Area × Volume) for the continuous power output, failing to multiply by the cycle frequency 'f'.

Additionally, a secondary trap tests the application of the Bohr model for hydrogen-like ions, where students often forget the Z² dependence for He⁺, leading to incorrect transition energies.

By explicitly excluding eddy currents, the problem isolates the hysteresis mechanism, forcing a direct equivalence between the macro-magnetic power and the quantum excitation rate.

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