As shown, a uniform magnetic field $B$ pointing out of paper plane is confined in the cylindrical region of cross-section radius r. At a distance $R$ from the center of shaded area there is point particle of mass m and carrying charge $q$. The magnetic field is then quickly changed to zero. The speed of particle just after magnetic field reduces to zero is?

Take: Initial magnetic field $B = 6T$
Charge $q = 80 mC$
Radius $r = 5\mathrm{cm}, R = 10\mathrm{cm}$
Mass of particle $= 2 \mathrm{gram}$.

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 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 $E\left(r\right)$?

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 $\left(C_{eq}= \frac{C_1{C}_2}{C_1+ C_2}\right)$

In a coil of resistance $100 \mathrm{\Omega }$, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil 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

A square frame of side $10 \mathrm{cm}$ and a long straight wire carrying current $1 \mathrm{A}$ are in the plane of the paper. Starting from close to the wire, the frame moves towards the right with a constant speed of $10 \mathrm{m} {\mathrm{s}}^{-1}$ (see figure). The e.m.f induced at the time the left arm of the frame is at $x=10 \mathrm{cm}$ from the wire is

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