A current carrying circular loop of radius 2 cm with unit normal $\hat{n}=\frac{\hat{k}+\hat{i}}{\sqrt{2}}$ is placed in a magnetic field, $\vec{B}=B_o(3 \hat{i}+2 \hat{k})$. If $B_o=4 \times 10^{-3} \mathrm{~T}$ and current $I=100 \sqrt{2} \mathrm{~A}$, the torque experienced by the loop is $\_\_\_\_$ Wb.A. ( $\pi=3.14$ )

A current of 30 A each flows in opposite directions in two conducting wires, placed parallel to each other at a distance of 8 cm . The magnetic field at the mid point between the two wires is $\_\_\_\_$ $\mu \mathrm{T}$.

$$ \left(\frac{\mu_{\mathrm{o}}}{4 \pi}=10^{-7} \mathrm{~N} / \mathrm{A}^2\right) $$

A small cube of side 1 mm is placed at the centre of a circular loop of radius 10 cm carrying a current of 2 A . The magnetic energy stored inside the cube is $\alpha \times 10^{-14} \mathrm{~J}$. The value of $\alpha$ is $\_\_\_\_$ .

$$ \left(\mu_{\mathrm{o}}=4 \pi \times 10^{-7} \mathrm{Tm} / \mathrm{A}, \pi=3.14\right) $$

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 $\_\_\_\_$ .