A conducting ring of radius $a$ is kept in $x-y$ plane with its centre at origin. A time varying magnetic field given by $\overrightarrow{B}=B_{0}t\left(-\hat{\mathrm{k}}\right)$ is applied in this region. An ideal voltmeter is connected between two points of the ring in two different cases as shown.

If $\pi B_0{a}^2=8 \mathrm{V}$ and voltmeter reading in case I and case II is $V_I$ and $V_{ll}$ respectively, then

The figure shows the cross section of a cylindrical region of radius $R$ in which the magnetic field points into the page. The magnitude of the field is $1 \mathrm{T}$ at time $t=0$ and it decreases to zero in $20$ seconds.

The induced electric field at a distance $r$ from the centre $O$ inside the cylindrical region is given by

The figure shows a circular area of tthe radius $R$ where a uniform magnetic field $\overrightarrow{B}$ is going into the plane of the paper and increasing in magnitude at a constant rate. In that case, which of the following graphs, drawn schematically, correctly shows the variation of the induced electric field $E\left(r\right)$?

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

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

Represent the union of two sets by Venn diagram for each of the following.

$X=\{x | x$ is a prime number between $80$ and $100\}$

$Y=\{y | y$ is an odd number between $90$ and $100\}$

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

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

A conducting ring of radius $1 \mathrm{m}$ is placed in a uniform magnetic field $B$, of $0.01 \mathrm{tesla}$ oscillating with frequency $100 \mathrm{Hz}$ with its plane at right angles to $\overrightarrow{B}$. What will be the induced electric field?