A vertical ring of radius $\mathrm{r}$ and resistance $\mathrm{R}$ falls vertically. It is in contact with two vertical rails which are joined at the top. The rails are without friction and resistance. There is a horizontal uniform magnetic field of magnitude $\mathrm{B}$ perpendicular to the plane of the ring and the rails. When the speed of the ring is $\mathrm{v}$, the current in the section $\mathrm{P}\mathrm{Q}$ is -

A thin strip $10 \mathrm{c}\mathrm{m}$ long is on a $\mathrm{U}$ shaped wire of negligible resistance and it is connected to a spring of spring constant $0.5 \mathrm{N}\mathrm{ }{\mathrm{m}}^{-1}$ (see figure). The assembly is kept in a uniform magnetic field of $0.1 \mathrm{T}.$ If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of $\mathrm{e}$ is $\mathrm{N}$ . If the mass of the strip is $50$ grams, its resistance $10\mathrm{\Omega }$ and air drag negligible, $\mathrm{N}$ will be close to:

A rod of length $2 \mathrm{m}$ slides with a speed of $5 \mathrm{m} {\mathrm{s}}^{-1}$ on a rectangular conducting frame as shown in figure. There exists a uniform magnetic field of $0.04 \mathrm{T}$ perpendicular to the plane of the figure. If the resistance of the rod is $3 \mathrm{\Omega }$. The current through the rod is

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:

A horizontal rod of length $L$ rotates about a vertical axis with a uniform angular velocity $\mathrm{\omega }$. A uniform magnetic field $B$ exists parallel to the axis of rotation. Then potential difference between the two ends of the rod is

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

As shown in the figure, a rectangular loop of a conducting wire is moving away with a constant velocity $v$ in a perpendicular direction from a very long straight conductor carrying a steady current $I$. When the breadth of the rectangular loop is very small compared to its distance from the straight conductor, how does the emf: $E$induced in the loop vary with time $t ?$

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: