Magnetic flux linked with the coil is given by $\phi(t) = 2t^2 + 2t + 1$ and its resistance is $10 \ \Omega$. The current passing through the coil at $t = 2 \ s$ is . . . . . . $A$.

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.

Use Lenz's law to determine the direction of induced current in the situations described by Figure:
$(a)$ $A$ wire of irregular shape turning into a circular shape;
$(b)$ $A$ circular loop being deformed into a narrow straight wire.

$A$ circular loop of radius $7 \ cm$ is placed in a uniform magnetic field of $0.2 \ T$ directed perpendicular to the plane of the loop. The loop is converted into a square loop in $0.5 \ s$. The $EMF$ induced in the loop is . . . . . . $mV$.

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 $t = 0.25\, s$?

$A$ magnetic field of flux density $1.0 \,Wb \,m^{-2}$ acts normal to a $80$ turn coil of $0.01 \,m^2$ area. If this coil is removed from the field in $0.2 \,s$, then the emf induced in it is (in $\,V$)