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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An infinitely long straight wire carrying current $I$, one side opened rectangular loop and a conductor $C$ with a sliding connector are located in the same plane, as shown in the figure. The connector has length $l$ and resistance $R$. It slides to the right with a velocity $v$. The resistance of the conductor and the self-inductance of the loop are negligible. The induced current in the loop, as a function of separation $r$, between the connector and the straight wire is:

A square-shaped conducting wire loop of dimension a moving parallel to the $x$-axis approaches a square region of size $b(a<b)$ where a uniform magnetic field $B$ exists pointing into the plane of the paper (see figure). As the loop passes through this region, the plot correctly depicting its speed $\left(v\right)$ as a function of $x$ is.

In the following circuit the switch $S$is closed at $t =0$. The charge on the capacitor $C_1$ as a function of time will be given by $\left(C_{eq}= \frac{C_1{C}_2}{C_1+ C_2}\right)$

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 $E\left(r\right)$?

A $1 \mathrm{m}$ long thin metal bar of negligible resistance weighing $1 \mathrm{kg}$ rests on two metal supports as shown in the figure. The supports are connected in series to an ideal cell and a resistance. A uniform magnetic field $0.5 \mathrm{T}$ is applied in the region normal to the plane of the paper and into the paper. Maximum emf that the cell can have without breaking the circuit in volt is
(Acceleration due to gravity $=10 \mathrm{m} {\mathrm{s}}^{-2}$ )

A metallic rod of length $l$ is tied to a string of length $2l$ and made to rotate with angular speed $\omega$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field B in the region, the e.m.f. induced across the ends of the rod is:

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 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