A circular coil of radius $20 \mathrm{cm}$ and $20$ turns of wire is mounted vertically with its plane in magnetic meridian. A small magnetic needle (free to rotate about vertical axis) is placed at the center of the coil. It is deflected through $45°$ when a current is passed through the coil and in equilibrium (Horizontal component of earth's field is $0.34 \times {10}^{–4} \mathrm{T}$). The current in coil is

A coil $\mathrm{ACD}$of $\mathrm{N}$ turns & radius $\mathrm{R}$ carries a current of $\mathrm{I} \mathrm{Amp}$& is placed on a horizontal table. $\mathrm{K}$ is a very small horizontal conducting ring of radius $\mathrm{r}$ placed at a distance $\mathrm{Y}$ from the centre of the coil vertically above the coil $\mathrm{ACD}.$ Find an expression for the $\mathrm{EMF}$established when the ring $\mathrm{K}$ is allowed to fall freely. Express the $\mathrm{EMF}$ in terms of instantaneous speed $\mathrm{v}$& height $\mathrm{Y}.$

Figure shows a wire of resistance $\mathrm{R}$ sliding on two parallel, conducting fixed thick rails placed at a separation $l$. A magnetic field $\mathrm{B}$ exists in a direction perpendicular to the plane of the rails. The wire is moving with a constant velocity $v$. Find current through the wire

$\mathrm{AB}$ and $\mathrm{CD}$ are fixed conducting smooth rails placed in a vertical plane and joined by a constant current source at its upper end. $\mathrm{PQ}$ is a conducting rod which is free to slide on the rails. A horizontal uniform magnetic field exists in space as shown. If the rod $\mathrm{PQ}$ is released from rest then,

For the situation shown in the figure, flux through the square loop is :

Three infinite current carrying conductors are placed as shown in figure. Two wires carry same current while current in third wire is unknown. The three wires do not intersect with each other and all of them are in the plane of paper. Which of the following is correct about a point $P$ that is also in the same plane.

A coaxial cable is made up of two conductors. The inner conductor is solid and is of radius $R_1$ & the outer conductor is hollow of inner radius $R_2$ and outer radius $R_3$. The space between the conductors is filled with air. The inner and outer conductors are carrying currents of equal magnitudes and in opposite directions. Then the variation of magnetic field with distance from the axis is best plotted as