The alternating e.m.f. induced in the secondary coil of a transformer is mainly due to

$A$ magnetic field given by $B(t) = (0.2t - 0.05t^2) \text{ T}$ is directed perpendicular to the plane of a circular coil containing $25$ turns of radius $1.8 \text{ cm}$ and whose total resistance is $5 \Omega$. The power dissipation at $3 \text{ s}$ is nearly: (in $\text{ } \mu\text{W}$)

$A$ uniform magnetic field $B$ exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of $4 \, mm$ and a total length of $30 \, cm$. The magnetic field changes with time at a steady rate $dB/dt = 0.032 \, T s^{-1}$. The induced current in the loop is close to $.... A$ (Resistivity of the metal wire is $1.23 \times 10^{-8} \, \Omega m$).

$A$ point charge $Q$ is moving in a circular orbit of radius $R$ in the $x$-$y$ plane with an angular velocity $\omega$. This can be considered as equivalent to a loop carrying a steady current $I = \frac{Q\omega}{2\pi}$. $A$ uniform magnetic field along the positive $z$-axis is now switched on,which increases at a constant rate from $0$ to $B$ in one second. Assume that the radius of the orbit remains constant. The application of the magnetic field induces an emf in the orbit. The induced emf is defined as the work done by an induced electric field in moving a unit positive charge around a closed loop. It is known that,for an orbiting charge,the magnetic dipole moment is proportional to the angular momentum with a proportionality constant $\gamma$.
$1.$ The magnitude of the induced electric field in the orbit at any instant of time during the time interval of the magnetic field change is:
$(A)$ $\frac{BR}{4}$ $(B)$ $\frac{BR}{2}$ $(C)$ $BR$ $(D)$ $2BR$
$2.$ The change in the magnetic dipole moment associated with the orbit,at the end of the time interval of the magnetic field change,is:
$(A)$ $-\gamma BQR^2$ $(B)$ $-\gamma \frac{BQR^2}{2}$ $(C)$ $\gamma \frac{BQR^2}{2}$ $(D)$ $\gamma BQR^2$
Give the answer for question $1$ and $2$.

Which conclusion can we obtain from the fact that an $emf$ is induced in a stationary conductor placed in a time-varying magnetic field? Discuss the characteristics of the induced electric field.

Two concentric circular coils,$C_{1}$ and $C_{2}$,are placed in the $XY$ plane. $C_{1}$ has $500$ turns and a radius of $1\; cm$. $C_{2}$ has $200$ turns and a radius of $20\; cm$. $C_{2}$ carries a time-dependent current $I(t) = (5t^{2} - 2t + 3)\; A$,where $t$ is in $s$. The $emf$ induced in $C_{1}$ (in $mV$) at the instant $t = 1\; s$ is $\frac{4}{x}$. The value of $x$ is: