$A$ magnetic field is changing at the rate of $4 \, T/s$ in a circular region of $5 \, cm$ radius. The value of the induced electric field at a point $P$,which is $10 \, cm$ away from the center $O$ of the region,is ..... $V/m$.

In the given figure,the magnetic flux through the loop increases according to the relation $\phi_{B}(t) = 10t^{2} + 20t$,where $\phi_{B}$ is in milliwebers $(mWb)$ and $t$ is in seconds $(s)$. The magnitude of the current through the $R = 2\,\Omega$ resistor at $t = 5\,s$ is $....\,mA$.

In the diagram shown,a time-varying non-uniform magnetic field passes through a circular region of radius $R$. The magnetic field is directed outwards and it is a function of radial distance $r$ and time $t$ according to the relation $B = B_0rt$. What is the induced electric field strength at a radial distance $R/2$ from the center?

If magnetic field passing through a coil of area $0.1 \ m^2$ is changing according to the equation $B = 20 \sin \left( \frac{2 \pi t}{3} \right) \text{ tesla}$,find the magnitude of induced emf at $t = 0.5 \ s$.

$A$ rectangular wire loop of sides $8 \; cm$ and $2 \; cm$ with a small cut is moving out of a region of uniform magnetic field of magnitude $0.3 \; T$ directed normal to the loop. Suppose the loop is stationary but the current feeding the electromagnet that produces the magnetic field is gradually reduced so that the field decreases from its initial value of $0.3 \; T$ at the rate of $0.02 \; T \, s^{-1}$. If the cut is joined and the loop has a resistance of $1.6 \; \Omega$,how much power is dissipated by the loop as heat? What is the source of this power?

The figure shows a uniform magnetic field $B$ confined to a cylindrical volume,which is increasing at a constant rate. The instantaneous acceleration experienced by an electron placed at point $P$ is: