A square metal wire loop of side $20 \mathrm{cm}$ and resistance $1\mathrm{\Omega }$ is moved with a constant velocity ${\mathrm{v}}_0$ in a uniform magnetic field $\mathrm{B}=4 \mathrm{Wb}/{\mathrm{m}}^2$  perpendicular to the plane of the loop and directed inwards. The loop is connected to a network of resistors as shown. If the resistance of load wires $\mathrm{AB}$ and $\mathrm{CD}$ are negligible, find the speed of the loop required to get a current of $2 \mathrm{mA}.$

 

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 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 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 $t ?$

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 conducting bar of length $L$ is free to slide on two parallel conducting rails as shown in the figure.

Two resistors $R_1$ and $R_2$ are connected across the ends of the rails. There is a uniform magnetic field $\overrightarrow{B}$ pointing into the page. An external agent pulls the bar to the left at a constant speed $v$.

The correct statement about the directions of induced currents $I_1$ and $I_2$ flowing through $R_1$ and $R_2$ respectively 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: