The magnetic flux passing perpendicular to the plane of the coil and directed into the paper is varying according to the relation $\phi = 3t^2 + 2t + 3$,where $\phi$ is in milliwebers $(mWb)$ and $t$ is in seconds $(s)$. The magnitude of the $emf$ induced in the loop when $t = 2 \ s$ is ...... $mV$.

$A$ coil of effective area $3 \text{ m}^2$ is placed at right angles to a magnetic field of induction $0.05 \text{ Wb/m}^2$. If the field is decreased to $20\%$ of its original value in $10 \text{ seconds}$, the e.m.f. induced in the coil will be (in $\text{ mV}$)

$A$ conducting loop is kept perpendicularly in an increasing magnetic field,as shown in the figure. The direction of the induced current in the loop will be:

$A$ coil of $n$ turns and area $A$ is suddenly removed from a magnetic field,and a charge $q$ flows through the coil. If the resistance of the coil is $R$,then the magnetic flux density is (in $Wb/m^2$):

An induced current of $2 \text{ A}$ flows through a coil. The resistance of the coil is $10 \text{ } \Omega$. What is the change in magnetic flux associated with the coil in $1 \text{ ms}$?

$A$ 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?