JEE PYQ: Electromagnetic Induction Question 10
Question 10 - 2020 (07 Jan Shift 1)
A long solenoid of radius $R$ carries a time ($t$)-dependent current $I(t) = I_0(1 - t)$. 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:
(1) Direction of $I_R$ remains unchanged and $V_R$ is maximum at $t = 0.5$
(2) At $t = 0.25$ direction of $I_R$ reverses and $V_R$ is maximum
(3) Direction of $I_R$ remains unchanged and $V_R$ is zero at $t = 0.25$
(4) At $t = 0.5$ direction of $I_R$ reverses and $V_R$ is zero
Show Answer
Answer: (4)
Solution
$I(t) = I_0(1-t) - I_0 t^2$… Actually $\phi = B \cdot A = (\mu_0 n I) \times (\pi R^2)$. $V_R = -\frac{d\phi}{dt} = \mu_0 n \pi R^2 (I_0 - 2I_0 t)$. $V_R = 0$ at $t = \frac{1}{2}$, and the direction of $I_R$ reverses at $t = 0.5$.
BETA
