General principle. Induced EMF appears only when the area of the loop inside the field region $x>0$ changes with time. While the loop sweeps through the field with constant entry/exit area, $i$ is constant; when it is entirely outside or entirely inside, $i=0$.

(P) Semicircular loop initially in $x<0$. Starts at ${\theta }_0=0$; as it rotates, area inside field grows at a constant rate (semicircle pivoting about its straight edge), giving a constant non-zero current during one half-period and zero current when fully outside. This matches a single rectangular pulse over T/2 to T: P $\to$ 3.

(Q) Wedge initially making 60° with the field boundary. The constant-rate entry begins immediately after a small delay (${\theta }_0=T/3$ to align with the field edge) and lasts for a fraction $T/6$, producing a pulse structure with successive positive and negative pulses as the wedge enters and exits multiple times per cycle: Q $\to$ 2.

(R) Small triangular loop initially aligned along the field edge. Begins entering at $t=0$ and exits at $T/6$, giving a single short rectangular pulse during 0–T/2 (with the corresponding return pulse cancelled in this geometry): R $\to$ 1.

(S) Symmetric two-lobe loop straddling the field edge. Whatever flux enters one lobe leaves the other simultaneously, so the net EMF cancels: $i(t)=0$ throughout. S $\to$ 4.

Mapping P $\to$ 3, Q $\to$ 2, R $\to$ 1, S $\to$ 4 corresponds to option (C).