The magnetic flux through a coil perpendicular to its plane and directed into the paper is varying according to the relation $\phi = 5t^2 + 10t + 5$ milliweber. The $e.m.f.$ induced in the loop after $5 \, s$ is ..... $V$.

Three resistances of magnitude $R$ each are connected in the form of an equilateral triangle of side $a$. The combination is placed in a magnetic field $B = B_0 e^{-\lambda t}$ perpendicular to its plane. The induced current in the circuit is given by:

$A$ bar magnet is moved along the axis of a copper ring placed far away from the magnet. Looking from the side of the magnet,an anticlockwise current is found to be induced in the ring. Which of the following may be true?

$A$ coil of circular cross-section having $1000$ turns and $4 \, cm^2$ face area is placed with its axis parallel to a magnetic field which decreases by $10^{-2} \, Wb \, m^{-2}$ in $0.01 \, s$. The $e.m.f.$ induced in the coil is....$mV$

$A$ 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?

The magnetic flux linked with a coil varies with time as $\Phi = 4t^2 + 3t + 7$. The magnitude of the induced e.m.f. at $t = 2 \ s$ is: (in $V$)