The current through a coil varies according to the following graph. Plot the graph for induced $emf$ $(e)$ versus time $(t)$ for the coil.

$A$ coil is placed in a magnetic field of $1 \, T$. Its area changes at a rate of $\frac{5 \, m^2}{ms}$. If the current in the coil changes from $1 \, A$ to $2 \, A$ in $2 \times 10^{-3} \, s$,what is the inductance of the coil in $H$?

$A$ small bar magnet of dipole moment $M$ is moving with speed $v$ along the $x$-direction towards a small closed circular conducting loop of radius $a$ with its centre $O$ at $x=0$ (see figure). Assume $x >> a$ and the coil has a resistance $R$. Which of the following statement$(s)$ is/are true?

Which of the following is a wrong statement?

$A$ square loop of side $12 \; cm$ with its sides parallel to $X$ and $Y$ axes is moved with a velocity of $8 \; cm \, s^{-1}$ in the positive $x$-direction in an environment containing a magnetic field in the positive $z$-direction. The field is neither uniform in space nor constant in time. It has a gradient of $10^{-3} \; T \, cm^{-1}$ along the negative $x$-direction (that is, it increases by $10^{-3} \; T \, cm^{-1}$ as one moves in the negative $x$-direction), and it is decreasing in time at the rate of $10^{-3} \; T \, s^{-1}$. Determine the direction and magnitude of the induced current in the loop if its resistance is $4.50 \; m\Omega$.

An electron is moving in a circular orbit of radius $R$ with an angular acceleration $\alpha$. At the centre of the orbit is kept a conducting loop of radius $r$ $(r \ll R)$. The $e.m.f.$ induced in the smaller loop due to the motion of the electron is