Induced Electric Field

As shown in the above figure, there is a uniform magnetic induction $B$ parallel to the axis of a cylindrical space of radius $R$. Plot the graph between the induced electric field and distance $r$ from the axis of the cylinder, if it is known that the rate of change of magnetic induction is constant.

As shown in the above figure, consider a closed-loop held in a magnetic field. The change in the magnetic flux linked with the loop induces a voltage $V$ in the loop. Now, find the work done in taking a charge $Q$ over a complete loop:

Cotyledons are also called-

A uniform magnetic field of induction $B$ is confined in a cylindrical region of the radius $R$. If the field is increasing at a constant rate of $\frac{\mathit{d}\mathit{B}}{\mathit{d}\mathit{t}}\mathit{=}\alpha \mathrm{T} {\mathrm{s}}^{-1}$, then the intensity of the electric field induced at a point $P$ distant $r$ from the axis as shown in the figure is equal to

A uniform but time varying magnetic field exists in cylindrical region and directed into the paper. If field decreases with time and a positive charge is placed at any point inside the region, then it moves
  

Two small pith balls, each carrying a charge $q$ are attached to the ends of a light rod of length $d$, which is suspended from the ceiling by a thin torsion-free fiber as shown in the figure. There is a uniform magnetic field $B$ pointing straight down, in the cylindrical region of radius $R$ around the fiber. The system is initially at rest. If the magnetic field is turned off, which of the following happens to the system?

Two small pith balls, each carrying a charge $\mathrm{q}$ are attached to the ends of a light rod of length $\mathrm{d}$, which is suspended from the ceiling by a thin torsion free fibre as shown in figure. There is a uniform magnetic field $\mathrm{B}$ pointing straight down, in the cylindrical region of radius $\mathrm{R}$ around the fibre. The system is initially at rest. If the magnetic field is turned off, which of the following happen to the system -

Two identical conductors of copper and aluminium are placed in identical electric fields. The magnitude of an induced charge in aluminium will be

Which of the field pattern given in the figure is valid for electric field as well as for magnetic field?

A cylindrical space of radius $R$, is filled with a uniform magnetic induction $B$, parallel to the axis of the cylinder. If $B$ changes at a constant rate, the graph showing the variation of induced electric field with distance $r$, from the axis of cylinder, is

A uniform but time-varying magnetic field $B\left(t\right)$ exists in a circular region of radius $a$ and is directed into the plane of the paper as shown. The magnitude of the induced electric field at point $P$ (outside the circular region) at a distance $r$ from the centre of the circular region
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Two identical circular loops of metal wire are lying on a table without touching each other. Loop $A$ carries a current which increases with time. In response, the loop $B$,