The coil of area $0.1 \ m^2$ has $500$ turns. After placing the coil in a magnetic field of strength $4 \times 10^{-4} \ Wb/m^2$,if it is rotated through $90^o$ in $0.1 \ s$,the average emf induced in the coil is......$V$

$A$ 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 $R$.

$A$ physicist works in a laboratory where the magnetic field is $2 \, T$. She wears a necklace enclosing an area of $0.01 \, m^2$ in such a way that the plane of the necklace is normal to the field,and it has a resistance $R = 0.01 \, \Omega$. Because of a power failure,the magnetic field decays to $1 \, T$ in $10^{-3} \, s$. What is the total heat produced in her necklace in Joules?

When a bar magnet is pushed towards the coil,along its axis,as shown in the figure,the galvanometer pointer deflects towards $X$. When this magnet is pulled away from the coil,the galvanometer pointer:

$A$ 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

Magnetic flux $\phi$ (in weber) linked with a closed circuit of resistance $10\, \Omega$ varies with time $t$ (in seconds) as $\phi = 5t^2 - 4t + 1$. The induced electromotive force in the circuit at $t = 0.2\, s$ is ......... $V$.