Match the following conditions for a long solenoid with a small coil placed coaxially inside it, with the nature of the induced EMF in the small coil. List - I List - II (P) Current in solenoid I = I

Question

Match the following conditions for a long solenoid with a small coil placed coaxially inside it, with the nature of the induced EMF in the small coil.

List - I	List - II
(P) Current in solenoid $I = I_{0} t$	(1) Induced EMF is zero
(Q) Current in solenoid $I = I_{0} sin (ω t)$	(2) Induced EMF is constant
(R) Current in solenoid $I = I_{0} e^{- k t}$	(3) Induced EMF is sinusoidal
(S) Current in solenoid $I = I_{0}$ (constant)	(4) Induced EMF decreases exponentially

TestHub · Accepted Answer

The induced EMF E = − M d t d I ​ , where M is the mutual inductance. For P, d I / d t = I 0 ​ (constant), so E is constant (P-2). For Q, d I / d t = I 0 ​ ω cos ( ω t ) (sinusoidal), so E is sinusoidal (Q-3). For R, d I / d t = − k I 0 ​ e − k t (exponentially decreasing), so E decreases exponentially (R-4). For S, d I / d t = 0 , so E is zero (S-1).

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