Discussion
List-I contains four conducting loops lying in the \(XY\) plane, as shown in the figures. The loops are rotating about \(Z\) axis passing through the point \(O\) with time period \(T\) in clockwise direction. The region \(x \gt 0\) contains a uniform magnetic field \(B\) in the \(+z\) direction. List-II contains the qualitative variation of the induced current \(i(t)\) for each of these loops. Choose the option which describes the correct match between the entries in List-I to those in List-II.
List-I
List-II
Answer: C
The correct match is P → 3, Q → 2, R → 1, S → 4.
The emf is proportional to the rate of change of the flux through the part of the loop lying in \(x \gt 0\), and the current follows its sign. The loop turns clockwise through \(\omega t\).
(P) A half-disc moves into the field region at a steady rate: the field-filled area grows linearly during the first half period and shrinks linearly during the second. The emf is constant and reverses at \(\frac{T}{2}\): graph (3).
(R) A single 60° sector enters the field during the first sixth of the period, stays fully inside (constant flux, no current), then leaves between \(\frac{T}{2}\) and \(\frac{2T}{3}\): one positive pulse, a gap, then one negative pulse: graph (1).
(S) The two sectors lie opposite each other, so one leaves the field exactly as the other enters, and the total flux stays constant: no current, graph (4).
(Q) The two sectors enter and leave at different times, giving two pulses of each sign: graph (2), the only one left.
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