Two long and parallel wires are at a distance of $0.1\, m$ and a current of $5\, A$ is flowing in each of these wires. The force per unit length due to these wires will be

$A$ rigid square loop of side $a$ carrying current $I_2$ is lying on a horizontal surface near a long wire carrying current $I_1$ in the same plane as shown in the figure. The net force on the loop due to the wire will be:

$A$ current of $5 \ A$ is flowing in a wire of length $1.5 \ m$. $A$ force of $7.5 \ N$ acts on it when it is placed in a uniform magnetic field of $2 \ T$. The angle between the magnetic field and the direction of the current is......$^o$

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 . . . . . . $\text{mN}$.

$A$ thin uniform rod with negligible mass and length $l$ is attached to the floor by a frictionless hinge at point $P$. $A$ horizontal spring with force constant $k$ connects the other end to a wall. The rod is in a uniform magnetic field $B$ directed into the plane of the paper. What is the extension in the spring in equilibrium when a current $i$ is passed through the rod in the direction shown? Assume the spring is initially at its natural length.

$AB$ 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.