A2 Daily A Level Physics question
A flat rectangular coil with 50 turns rotates at a constant angular speed within a uniform magnetic field. This induces a sinusoidal e.m.f. across the coil with a peak value of V₀. This coil is then replaced by a second coil that has 100 turns but half the cross-sectional area of the first coil. The second coil is rotated at the same constant angular speed in the same magnetic field. What is the peak value of the e.m.f. induced in the second coil?
Answer
The correct answer is A.
Correct: A — V₀. The peak induced e.m.f. is proportional to the rate of change of magnetic flux linkage. For a rotating coil, this peak e.m.f. is proportional to the product of the number of turns (N) and the coil's cross-sectional area (A), as well as the field strength and angular speed which are constant here. The number of turns is doubled (50 → 100), while the area is halved (A → A/2). The new product is (2N) × (A/2) = NA, which is the same as the original. Therefore, the peak e.m.f. is unchanged. B is incorrect as it only considers the doubling of the number of turns, ignoring the halving of the area. C is incorrect as it only considers the halving of the area, ignoring the doubling of the number of turns. D is incorrect as it would imply a faulty relationship where the e.m.f. is proportional to N/A, leading to a factor of (2N)/(A/2) = 4.