Question 15

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 $$x>0$$ 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.

(P) $$\phi = (\frac{1}{2}R^2 \times \theta) \times B = \frac{1}{2} R^2 (\omega t) B$$

$$\varepsilon = -\frac{d\phi}{dt} = -\frac{1}{2}BR^2 \omega =$$ constant

Graph (3)

(Q) Graph similar to (P) but punctuated $$\Rightarrow$$ Graph (2)

(R) Graph similar to (P) but some part $$\varepsilon = 0$$ $$\Rightarrow$$ Graph (1)

(S) $$\frac{d\phi}{dt} = 0 = \varepsilon$$ for all time $$\Rightarrow$$ Graph (4)

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