A metal rod of mass $10 \mathrm{gm}$ and length $25 \mathrm{cm}$ is suspended on two springs as shown in the figure. The springs are extended by $4 \mathrm{cm}$. When a $20 \mathrm{ampere}$ current passes through the rod it rises by $1 \mathrm{cm}$. Determine the magnetic field assuming acceleration due to gravity to be $10 \mathrm{m} {\mathrm{s}}^{-2}$.

Let $F_A$ and $F_B$ be the magnitude of the force between the two wires in setup $A$ and setup $B$, respectively.

A rigid square loop of side $\mathrm{‘}\mathrm{a}’$ and carrying current ${\mathrm{I}}_2$ is lying on a horizontal surface near a long current ${\mathrm{I}}_1$ carrying wire in the same plane as shown in figure. The net force on the loop due to the wire will be:

An arrangement of three parallel straight wires placed perpendicular to plane of paper carrying same current $I$ along the same direction is shown in Figure. Magnitude of force per unit length on the middle wire $B$ is given by

Consider two straight parallel conductors $A$ and $B$ separated by a distance $x$ and carrying individual currents $i_A \mathrm{a}\mathrm{n}\mathrm{d}\mathrm{ }{i}_B$ respectively. If the two conductors attract each other, it indicates that

A copper rod of mass $m$ slides under gravity on two smooth parallel rails $l$ distance apart and set an angle $\theta$ to the horizontal. At the bottom, the rails are joined by a resistance $R$ in figure. There is a uniform magnetic field $B$ perpendicular to the plane of the rails. The terminal velocity of rod is

The magnitude and direction of a force vector acting on a unit length of thin wire carrying a current $I$ at point $O$, if the wire has a semicircular shape of radius $R$ as shown in the figure.

Two long conductors, separated by a distance $d$ carry currents $I_1$  and $I_2$ in the same direction. They exert a force $F$ on each other. Now the current in one of them is increased to two times and its direction is reversed. The distance is also increased to $3d$. The new value of force between them is

Two long straight parallel wires, carrying (adjustable) currents $I_1$ and $I_2$ , are kept at a distance $d$ apart. If the force $F$ between the two wires is taken as 'positive' when the wires repel each other and 'negative' when the wires attract each other, the graph showing the dependence of $F$, on the product $I_1{I}_2$ , would be: