The magnetic field varies as $B = B_0 e^{-t}$. The coil has a radius $r$ and resistance $R$. What is the power dissipated when the key $K$ is closed at $t = 0$?

$A$ rectangular loop is being pulled at a constant speed $v$,through a region of certain thickness $d$,in which a uniform magnetic field $B$ is set up. The graph between position $x$ of the right-hand edge of the loop and the induced emf $E$ will be

Radio frequency choke uses a core of

The figure shows three circuits with identical batteries,inductors,and resistors. Rank the circuits according to the current through the battery $(i)$ just after the switch is closed and $(ii)$ a long time later,greatest first.

$A$ metallic square wire loop of side $10\, cm$ and resistance $1\,\Omega$ is moved with a constant velocity $v_0$ in a uniform magnetic field of induction $B = 2\, T$ as shown in the figure. The magnetic field is perpendicular into the plane of the loop. The loop is connected to a network of resistors each of value $3\,\Omega$. The resistance of the lead wires $OS$ and $PQ$ are negligible. What should be the speed of the loop so as to have a steady current of $1\, mA$ in it? Give the direction of current in the loop.

$A$ conducting loop in the form of a circle is placed in a uniform magnetic field with its plane perpendicular to the direction of the field. An emf will be induced in the loop, if