A metal coil of area $A,$ number of turns $n,$ mass $m$ and resistance $r$ is lying in a horizontal plane. A uniform time varying magnetic field is set-up to pass vertically through the coil at time $t=0$. The field is first increased from $0$ to $B_0$ at a constant rate in time $t_0$ and then decreased from $B_0$ to zero in the same time $t_0$. If the cycle is repeated continuously, then the correct graph(s) representing the variation of current and power dissipated with time $\left(t\right)$ is/are

Two magnetic dipoles $\mathrm{X}$ and $\mathrm{Y}$ are placed at a separation $\mathrm{d}$ , with their axes perpendicular to each other. The dipole moment of $\mathrm{Y}$ is twice that of $\mathrm{X}$ . A particle of charge $\mathrm{q}$ is passing through their mid-point $\mathrm{P}$ , at angle $\mathrm{\theta }={45}^{\mathrm{o}}$ with the horizontal line, as shown in figure. What would be the magnitude of force on the particle at that instant? ( $\mathrm{d}$ is much larger than the dimension of the dipole)

For a plane electromagnetic wave, the magnetic field at a point $\mathrm{x}$ and time $\mathrm{t}$ is :

$\overrightarrow{\mathrm{B}}\left(\mathrm{x},\mathrm{t}\right)=\left[1.2\times {10}^{-7}\sin \left(0.5\times {10}^3\mathrm{x}+1.5\times {10}^{11}\mathrm{t}\right)\hat{\mathrm{k}}\right] \mathrm{T}$.

The instantaneous electric field $\overrightarrow{\mathrm{E}}$ corresponding to $\overrightarrow{\mathrm{B}}$ is :

An electron enters a magnetic field of $\left(3 \hat{i}+4 \hat{j}\right) \mathrm{T}$ with a velocity of $\left(6 \hat{j}+4 \hat{k}\right) \mathrm{m} {\mathrm{s}}^{-1}.$ The acceleration produced is

($\frac{e}{m}$ of electron $=1.76\times {10}^{11} \mathrm{C} {\mathrm{kg}}^{-1}$)

What is the importance of Oersted's experiment?