Question

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 :

• A. Direction of $I_R$ remains unchanged and $V_R$ is zero at $t =0.25$
• B. Direction of $I_R$ remains unchanged and $V_R$ is maximum at $t = 0.5$
• C. At $t =0.25$ direction of $I_R$ reverses and $V_R$ is maximum
• D. At $t = 0.5$ direction of $I_R$ reverses and $V_R$ is zero

Answer 1

Answer: (D)

$I=I_{0}t-I_{0}t^{2}$
$\phi=BA$
$\phi=\mu_{0}nIA$
$V_{R}=-\frac{d\phi}{dt}=-\mu_{0}nAI_{0}\left(1-2t\right)$
$V_{R}=0 at t=\frac{1}{2}$
and $I_{R}=\frac{V_{R}}{Resistance \,of \,loop}$