The figure shows a conducting loop placed in a magnetic field. The magnetic flux through the loop changes according to the equation $\phi = 5t - 10t^2$. What is the direction and magnitude of the induced current at $t = 0.25\, s$?

When the switch is closed in the primary circuit,the instantaneous induced current in the secondary 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 $R$.

Assertion $(A)$: It is more difficult to move a magnet into a coil with more loops.
Reason $(R)$: This is because the emf induced in each current loop resists the motion of the magnet.

If a coil of $40$ turns and area $4.0 \, cm^2$ is suddenly removed from a magnetic field,it is observed that a charge of $2.0 \times 10^{-4} \, C$ flows through the coil. If the resistance of the coil is $80 \, \Omega$,the magnetic flux density in $Wb/m^2$ is:

$A$ copper ring having a cut such as not to form a complete loop is held horizontally and a bar magnet is dropped through the ring with its length along the axis of the ring as shown in figure. The acceleration of the falling magnet is ($g=$ acceleration due to gravity)