Which of the following does not induce an emf in the loop?

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Question: Which of the following does not induce an emf in the loop?

Option a: Decreasing the area of the loop
- Explanation: The magnetic flux through the loop is Φ = B · A · cosθ. If the area A decreases while B and θ stay fixed, Φ decreases proportionally, which by Faraday's law induces an emf (ε = -dΦ/dt). So this option would induce an emf.

Option b: Increasing the number of turns of the loop
- Explanation: For a coil with N turns, the total flux linkage is N · Φ. If N increases while Φ remains the same, the flux linkage changes, producing an emf according to ε = -d(NΦ)/dt = -Φ · dN/dt (assuming Φ is not changing due to other factors). Therefore increasing the number of turns also induces an emf.

Option c: Decreasing the magnetic field
- Explanation: If B decreases while the loop’s area and orientation are fixed, the flux Φ = B · A · cosθ decreases, leading to an emf by Faraday’s law. So this option induces an emf.

Option d: Increasing the angle between the magnetic field and the normal to the loop
- Explanation: The flux is Φ = B · A · cosθ. Increasing θ reduces cosθ, hence reduces Φ if B, A, and θ change with time. This change in flux induces an emf as well. So this option induces an emf.

Overall, every option a, b, c, and d describes a situation that changes magnetic flux through the loop (or flux linkage in the case of multiple turns), which by Faraday’s law induces an emf. Therefore, strictly speaking, none of the options does not induce an emf; all of them can induce emf if the stated quantity changes with time. The provided answer choice stating b as “does not induce emf” contradicts the fundamental relation ε = -dΦ/dt (and, for coils, ε includes the dN/dt term as well).

UCIC 202503 PHYS101 Quiz 11

Which of the following does not induce an emf in the loop?

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