$A$ 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 $mm$)

An arbitrarily shaped closed coil is made of a wire of length $L$ and a current $I$ ampere is flowing in it. If the plane of the coil is perpendicular to a uniform magnetic field $\vec{B}$, the net magnetic force on the coil is

Three parallel wires $a$,$b$,and $c$ carrying currents $i_a$,$i_b$,and $i_c$ as shown in the figure are placed next to each other. The magnitude of the force on a length $l$ of the wire $a$,if $d_2 = 2 d_1$,$i_b = i_a$,and $i_c = 4 i_a$ is:

$AB$ 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.

$A$ straight wire is placed in a magnetic field that varies with distance $x$ from the origin as $\vec{B} = B_0 \left( 2 - \frac{x}{a} \right) \hat{k}$. The ends of the wire are at $(a, 0)$ and $(2a, 0)$ and it carries a current $I$ in the positive $x$-direction. If the force on the wire is $\vec{F} = IB_0 \left( \frac{ka}{2} \right) \hat{j}$,then the value of $k$ is:

The figure shows a cross-section of an infinite metal sheet carrying an electric current along its surface. The current per unit length is $J$. $A$ current-carrying square loop is placed nearby the metal sheet such that the plane of the square is perpendicular to the plane of the sheet. Then: