Q 12-06-118JEE MainJEE Main 2020 (7 Jan, Shift 1)Medium
A long solenoid of radius $R$ carries a time ($t$) dependent current $I(t) = I_0t(1 - t)$. A ring of radius $2R$ is placed coaxially near its middle. During the time interval $0 \le t \le 1$, the induced current ($I_R$) and the induced EMF ($V_R$) in the ring change as:
Answer: (D) At $t = 0.5$ direction of $I_R$ reverses and $V_R$ is zero
The flux through the ring is the flux inside the solenoid: $\Phi = \mu_0nI\pi R^2$ (there is no field outside a long solenoid).
$$V_R = -\frac{d\Phi}{dt} = -\mu_0n\pi R^2I_0(1 - 2t)$$
This is zero at $t = 0.5$ and changes sign there, so the induced current reverses direction at $t = 0.5$.
Solution by Sreeraj P, M.Sc Physics