$A$ coil having effective area '$A$' is held with its plane normal to a magnetic field of induction '$B$'. The magnetic induction is quickly reduced to $25\%$ of its initial value in $1 \text{ s}$. The e.m.f. induced in the coil (in volt) will be

Suppose a long solenoid of $100 \ cm$ length, radius $2 \ cm$ having $500 \ turns/cm$ carries a current $I = 10 \sin(\omega t) \ A$, where $\omega = 1000 \ rad/s$. $A$ circular conducting loop $(B)$ of radius $1 \ cm$ is coaxially placed inside the solenoid. The r.m.s. current through the loop when the coil $B$ is inside the solenoid is $\alpha / \sqrt{2} \ \mu A$. The value of $\alpha$ is . . . . . . . [Resistance of the loop $= 10 \ \Omega$]

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.

$A$ coil of resistance $250 \Omega$ is placed in a magnetic field. If the magnetic flux $(\phi)$ linked with the coil varies with time $t$ $(s)$ as $\phi = 50t^2 + 7$,the current in the coil at $t = 4 \ s$ is: (in $A$)

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 $t = 0.25\, s$?

The Lenz law is associated with