Induced Electric Field

The circular wire in figure below encircles solenoid in which the magnetic flux is increasing at a constant rate out of the plane of the page.

The clockwise emf around the circular loop is ${\epsilon }_0.$ By definition a voltammeter measures the voltage difference between the two points given
by $V_b-V_a=-{\int }_a^b\overrightarrow{E}·\mathrm{d}\overrightarrow{s}.$ We assume that $a$ and $b$are infinitesimally close to each other. The values of $V_b-V_a$ along the path $1$ and $V_a-V_b$ along the path $2,$ respectively are

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:

As shown in the above figure, a loop surrounds three regions of the magnetic field where the magnitude of the magnetic field is decreasing at a constant rate $\alpha$. Take the area of each region as $A$. Now find the $\oint \overrightarrow{\mathit{E}}\mathit{.}\overrightarrow{\mathit{d}\mathit{l}}$ along the given loop, where $\overrightarrow{\mathit{E}}$ is the induced electric field.

Consider the uniform magnetic field of magnitude $0.01 \mathrm{T}$ directed perpendicularly to the plane of a conducting ring of the radius $1 \mathrm{m}$. If the ring is oscillating with a frequency of $0.1 \mathrm{kHz}$, then find the induced electric field.

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 conductor is moving with velocity v in a region of uniform magnetic field B. The electric field at P inside conductor is

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

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 -

As a result of change in magnetic flux linked with the closed loop shown in the figure, an emf $V\mathrm{ }\mathrm{v}\mathrm{o}\mathrm{l}\mathrm{t}$ is induced in the loop. The work done in taking a charge, $Q \mathrm{coulomb}$, once along the loop is,

The resistance in the following circuit is increased at a particular instant. At this instant the value of resistance is $10 \mathrm{\Omega }$. The current in the circuit will be now

A uniform but time-varying magnetic field $B\left(t\right)$ exists in a circular region of radius $\mathrm{a}$ and is directed into the plane of the paper as shown in the figure. The magnitude of the induced electric field at a point $P$ at a distance $\mathrm{r}$ from the centre of the circular region,

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

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 in the figure. The magnitude of an induced electric field at the point $P$ at a distance $r$ from the centre of the circular region

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

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 non-conducting ring of mass $m$ and radius $R$ has a charge $Q$ uniformly distributed over its circumference. The ring is placed on a rough horizontal surface such that plane of the ring is parallel to the surface. A vertical magnetic field $B=B_0{t}^2$ tesla is switched on. After $2 \mathrm{s}$ from switching on the magnetic field the ring is just about to rotate about vertical axis though its centre.

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 $B$,