$$ \text { Match List - I with List - II. } $$

Choose the correct answer from the options given below :

A metal rod of length $L$ rotates about one end at origin with a uniform angular velocity $\omega$. The magnetic field radially falls off as $B(\mathrm{r})=B_{\mathrm{o}} \mathrm{e}^{-\lambda r} ; \lambda$ being a positive constant. The emf induced (neglecting the centripetal force on electrons in the rod) is :

Under steady state condition the potential difference across the capacitor in the circuit is $\_\_\_\_$ V.

A particle of charge $q$ and mass $m$ is projected from origin with an initial velocity $\vec{v}=\left(\frac{v_0}{\sqrt{2}} \hat{x}+\frac{v_0}{\sqrt{2}} \hat{y}\right)$. There exists a uniform magnetic field $\vec{B}=B_0 \hat{z}$ and a space varying electric field $\vec{E}=E_{\mathrm{o}} \mathrm{e}^{-\lambda x} \hat{x}$ within the region $0 \leqslant x \leqslant L$. After travelling a distance such that $x$-coordinate has changed from $x=0$ to $x=L$, the change in the kinetic energy is $\_\_\_\_$ .