$A$ flat circular coil has $100$ turns of wire of radius $10 \ cm$. $A$ uniform magnetic field exists in a direction perpendicular to the plane of the coil and it grows at a rate of $0.1 \ T \ s^{-1}$. The induced emf in the coil is:

Assertion : Lenz's law violates the principle of conservation of energy.
Reason : Induced $emf$ always opposes the change in magnetic flux responsible for its production.

$A$ coil having $n$ turns and resistance $R \, \Omega$ is connected with a galvanometer of resistance $4 \, R \, \Omega$. This combination is moved in time $t$ seconds from a magnetic field $W_1$ weber to $W_2$ weber. The induced current in the circuit is

$A$ rectangular loop of wire $ABCD$ is kept close to an infinitely long wire carrying a current $I(t) = I_0(1 - t/T)$ for $0 \le t \le T$ and $I(t) = 0$ for $t > T$ as shown in the figure. Find the total charge passing through a given point in the loop in time $T$. The resistance of the loop is $R$.

$A$ bar magnet is allowed to fall vertically through a copper coil placed in a horizontal plane. The magnet falls with a net acceleration:

$A$ coil having $500$ square loops each of side $10 \ cm$ is placed normal to a magnetic flux which increases at a rate of $1 \ T s^{-1}$. The induced emf is (in $V$)