Currents of $10 \ A$ and $2 \ A$ are passed through two parallel wires $A$ and $B$ respectively in opposite directions. If the wire $A$ is infinitely long and the length of the wire $B$ is $2 \ m$,the force acting on the conductor $B$,which is situated at a distance of $10 \ cm$ from $A$,will be . . . . . . .

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 $10 \, cm$.

$A$ uniform magnetic field of $1.5\; T$ exists in a cylindrical region of radius $10.0\; cm$,its direction parallel to the axis along east to west. $A$ wire carrying current of $7.0\; A$ in the north to south direction passes through this region. What is the magnitude and direction of the force on the wire if,
$(a)$ the wire intersects the axis,
$(b)$ the wire is turned from $N-S$ to northeast-northwest direction,
$(c)$ the wire in the $N-S$ direction is lowered from the axis by a distance of $6.0 \;cm?$

$A$ wire carrying a current $I$ along the positive $x$-axis has length $L$. It is kept in a magnetic field $\overrightarrow{B} = (2\hat{i} + 3\hat{j} - 4\hat{k}) \text{ T}$. The magnitude of the magnetic force acting on the wire is $..........IL$.

$A$ wire $AB$ is carrying a steady current $I_1$ and is kept on a table. Another wire $CD$ carrying current $I_2$ is held directly above it at a distance $r$. When the wire $CD$ is left free and it remains suspended at its position, find its mass per unit length. (Given: $g$ = acceleration due to gravity, $\mu_0$ = permeability of free space)

$A$ horizontal rod of mass $10 \, g$ and length $10 \, cm$ is placed on a smooth plane inclined at an angle of $60^\circ$ with the horizontal,with the length of the rod parallel to the edge of the inclined plane. $A$ uniform magnetic field of induction $B$ is applied vertically downwards. If the current through the rod is $1.73 \, A$,then the value of $B$ for which the rod remains stationary on the inclined plane is......$T$