$A$ coil of $n$ turns and resistance $R \ \Omega$ is connected in series with a resistance $R/2$. The combination is moved for time $t$ seconds through a magnetic flux change from $\Phi_1$ to $\Phi_2$. The induced current in the circuit is:

$A$ system $S$ consists of two coils $A$ and $B$. The coil $A$ carries a steady current $I$. The coil $B$ is suspended nearby as shown in the figure. If the system is heated,so as to raise the temperature of the two coils steadily,then:

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.

Magnetic flux (in $Wb$) linked with a closed loop varies with time $t$ (in $s$) as $\phi = 2t^2 + 1$. The magnitude of induced emf at $t = 1 \ s$ is $..... \ V$.

$A$ line charge ($\lambda$ per unit length) is in the form of a circular wheel of radius $a$ and moment of inertia $I$,initially at rest. It is free to rotate in a horizontal plane. There is a coaxial magnetic field $B = B_0 \hat{k}$ extending up to a radius $b$ $(b < a)$. If the magnetic field is switched off,the angular velocity $\omega$ of the wheel is given by:

$A$ coil having $n$ turns and resistance $R$ is connected with a galvanometer of resistance $2R$. This combination is moved in time $t$ from flux $\phi_1$ to $\phi_2 \ Wb$. The induced current in the circuit is