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 ...... $mV$.

$A$ circular coil of area $100 \,cm^2$ and $20$ turns is kept in a magnetic field of flux density $2 \,Wb/m^2$. It rotates from a position where its plane makes an angle of $30^{\circ}$ with the field to a position perpendicular to the field in a time $0.2 \,s$. Find the magnitude of the emf induced in the coil due to its rotation. (in $V$)

The negative sign in Faraday's law represents which fact?

$A$ magnetic field of $2 \times 10^{-2} \,T$ acts at right angles to a coil of area $100 \,cm^2$ with $50$ turns. The average e.m.f. induced in the coil is $0.1 \,V$, when it is removed from the field in time '$t$'. The value of '$t$' is

$A$ coil of area $100 \, cm^2$ has $500$ turns. $A$ magnetic field of $0.1 \, Wb/m^2$ is perpendicular to the coil. The field is reduced to zero in $0.1 \, s$. The induced $e.m.f.$ in the coil is $...... \, V$.

$A$ uniform magnetic field $B$ that is perpendicular to the plane of the page passes through the loops,as shown. The field is confined to a region of radius $a$,where $a < b$,and is changing at a constant rate. The induced $emf$ in the wire loop of radius $b$ is $\varepsilon$. What is the induced $emf$ in the wire loop of radius $2b$?