Question

A long solenoid of radius $R$ carries a time $\left(t\right)$ dependent current $I\left(t\right)=I_{0}t\left(1 - t\right)$ . A ring of radius $2R$ is placed coaxially near its middle. During the time interval $0\leq t\leq 1,$ the induced current $\left(I_{R}\right)$ and the induced $EMF\left(V_{R}\right)$ in the ring change as:

• A. Direction of $I_{R}$ remains unchanged and $V_{R}$ is maximum at $t=0.5$
• B. At $t=0.25$ direction of $I_{R}$ reverses and $V_{R}$ is maximum
• C. Direction of $I_{R}$ remains unchanged and $V_{R}$ is zero at $t=0.25$
• D. At $t=0.5$ direction of $I_{R}$ reverses and $V_{R}$ is zero

Answer 1

Answer: (D)

$I=I_{0}t-I_{0}t^{2}$
$\phi=BA$
$\phi=\mu _{0}nIA$
$V_{R}=-\frac{d \phi}{d t}=-\left(\mu \right)_{0}nAI_{0}\left(1 - 2 t\right)$
$V_{R}=0$ at $t=\frac{1}{2}$
And $I_{R}=\frac{V_{R}}{R e s i s t a n c e o f l o o p}=0$