A long solenoid of radius R carries a time (t) - dependent current I ( t )= I_0 t (1- t ). A ring of radius 2 R is placed coaxially near its middle.…

A long solenoid of radius $\displaystyle R$ carries a time (t) - dependent current $\displaystyle \mathrm{I}(\mathrm{t})=\mathrm{I}_0 \mathrm{t}(1-\mathrm{t})$. A ring of radius $\displaystyle 2$ R is placed coaxially near its middle. During the time interval $\displaystyle 0 \leq \mathrm{t} \leq 1$, the induced current $\displaystyle \left(\mathrm{I}_{\mathrm{R}}\right)$ and the induced $\displaystyle \operatorname{EMF}\left(\mathrm{V}_{\mathrm{R}}\right)$ in the ring change as :