$A$ short-circuited coil is placed in a time-varying magnetic field. Electrical power is dissipated due to the current induced in the coil. If the number of turns were to be quadrupled and the wire radius halved, the electric power dissipated would be .............

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:

$A$ non-conducting ring (of mass $m$,radius $r$,having charge $Q$) is placed on a rough horizontal surface in a region with a transverse magnetic field. The magnetic field is increasing with time at a rate $R = dB/dt$. If the coefficient of friction between the surface and the ring is $\mu$,for the ring to remain in equilibrium,$\mu$ should be greater than:

In the branch $AB$ of a circuit,as shown in the figure,a current $I = (t + 2) \ A$ is flowing,where $t$ is the time in seconds. At $t = 0$,the value of $(V_A - V_B)$ will be: (in $V$)

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.

The figure shows a circular area of radius $R$ where a uniform magnetic field $\vec B$ is directed into the plane of the paper and is increasing in magnitude at a constant rate. In this case,which of the following graphs,drawn schematically,correctly shows the variation of the induced electric field $E(r)$ with distance $r$ from the center?