$A$ long wire $AB$ is placed on a table. Another wire $PQ$ of mass $1.0\, g$ and length $50\, cm$ is set to slide on two rails $PS$ and $QR$. $A$ current of $50\, A$ is passed through the wires. At what distance above $AB$ will the wire $PQ$ be in equilibrium? (in $mm$)

$A$ rectangular loop of wire,supporting a mass $m$,hangs with one end in a uniform magnetic field $\overrightarrow{B}$ pointing into the plane of the paper. $A$ clockwise current $i$ is set up such that $i > mg/Ba$,where $a$ is the width of the loop. Then:

The magnetic field existing in a region is given by $\vec{B} = 0.2(1 + 2x) \hat{k} \text{ T}$. $A$ square loop of edge $50 \text{ cm}$ carrying $0.5 \text{ A}$ current is placed in the $x-y$ plane with its edges parallel to the $x-y$ axes,as shown in the figure. The magnitude of the net magnetic force experienced by the loop is . . . . . . $\text{mN}$.

Two long straight parallel conductors are carrying currents $i_1$ and $i_2$ in the same direction. The work done per unit length,when the distance between them is doubled,is:

Find the force per unit length at point $P$. The current in the wire is $5 \, A$ and the distance between the parallel segments is $10 \, cm$.

$A$ straight rod of mass $m$ and length $L$ is suspended from two identical springs as shown in the figure. The springs are stretched by a distance of $x_0$ due to the weight of the rod. The circuit has a total resistance $R$. When a magnetic field perpendicular to the plane of the paper is switched on,the springs are observed to extend further by the same distance $x_0$. The magnetic field strength is: