Physics
Physics
Problem
A conducting circular loop of radius lies in a uniform magnetic field of magnitude directed perpendicular to the plane of the loop. A student claims that an induced electromotive force (emf) can be obtained either by steadily decreasing the area of the loop or by keeping the area fixed and steadily rotating the loop about a diameter. Explain the following points in detail: (i) Why does a change in area of the loop produce an emf even though the magnetic field is steady? (ii) Why does a rotation of the loop about a diameter also produce an emf although the area enclosed by the loop remains constant? (iii) If, at a given instant, the magnitude of the rate of change of magnetic flux is the same for the two cases described above, compare the instantaneous directions of the induced currents in the loop for the two methods. Justify your answer using an appropriate law. (iv) The student further suggests that if the magnitude of the emf is the same in the two cases, the power dissipated in an external resistor connected to the loop must also be the same. Critically comment on this suggestion, stating any additional information that would be required to make such a comparison meaningful.Intuitive explanation
This problem tests your understanding of Faraday's law of electromagnetic induction and how the same rate of flux change can arise from fundamentally different physical mechanisms. The key insight is that depends only on how fast the magnetic flux through the loop changes, not why it changes—but the direction of induced current follows Lenz's law based on whether flux is increasing or decreasing. When comparing power dissipation, remember that emf magnitude alone doesn't determine power; the internal resistance of the loop (which depends on its geometry and material) also matters crucially.
Intuitive explanation
This problem tests your understanding of Faraday's law of electromagnetic induction and how the same rate of flux change can arise from fundamentally different physical mechanisms. The key insight is that depends only on how fast the magnetic flux through the loop changes, not why it changes—but the direction of induced current follows Lenz's law based on whether flux is increasing or decreasing. When comparing power dissipation, remember that emf magnitude alone doesn't determine power; the internal resistance of the loop (which depends on its geometry and material) also matters crucially.