Two wires $2 \text{ mm}$ apart supply current to a $100 \text{ V}$,$1 \text{ kW}$ heater. The force per metre between the wires is (Given $\mu_0 = 4\pi \times 10^{-7} \text{ T m/A}$)

An infinitely long,straight conductor $AB$ is fixed and a current $i_1$ is passed through it. Another movable straight wire $CD$ of finite length carrying current $i_2$ is held perpendicular to it and released. Neglect the weight of the wire.

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 $2$ times and its direction is reversed. The distance between them is also increased to $3d$. The new value of force between them is:

$A$ rigid wire consists of a semicircular portion of radius $R$ and two straight sections. The wire is partially immersed in a perpendicular magnetic field $B = B_0 \hat{k}$ as shown in the figure. The magnetic force on the wire if it carries a current $i$ is:

Define $1 \ A$ (Ampere) using the force between two current-carrying parallel wires.

$AB$ and $CD$ are smooth parallel rails,separated by a distance $l$,and inclined to the horizontal at an angle $\theta$. $A$ uniform magnetic field of magnitude $B$,directed vertically upwards,exists in the region. $EF$ is a conductor of mass $m$,carrying a current $i$. If the conductor is in equilibrium,find the relation between the given parameters.