There are two coils $A$ and $B$ as shown in the figure. No current flows in $B$ if $A$ is at rest. Now,the coil $A$ is made to rotate about a vertical axis. At the shown instant $(t=0)$,what will be the direction of the current in coil $A$,when the induced current in coil $B$ is counterclockwise?

The direction of induced e.m.f. during electromagnetic induction is given by

It is desired to measure the magnitude of the magnetic field between the poles of a powerful loudspeaker magnet. $A$ small flat search coil of area $2 \; cm^{2}$ with $25$ closely wound turns is positioned normal to the field direction and then quickly snatched out of the field region. (Equivalently,one can give it a quick $90^{\circ}$ turn to bring its plane parallel to the field direction). The total charge flown in the coil (measured by a ballistic galvanometer connected to the coil) is $7.5 \; mC$. The combined resistance of the coil and the galvanometer is $0.50 \; \Omega$. Estimate the field strength of the magnet.

$A$ coil of $45$ turns and radius $4 \ cm$ is placed in a uniform magnetic field such that its plane is perpendicular to the direction of the field. If the magnetic field increases from $0$ to $0.70 \ T$ at a constant rate in a time interval of $220 \ s$,then the induced emf in the coil is (in $mV$)

Two identical circular coils $A$ and $B$ are kept on a horizontal tube side by side without touching each other. If the current in the coil $A$ increases with time,in response,the coil $B$

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 $t = 0.25\, s$?