The magnetic field existing in a region is given by $\vec B = B_0 \left( 5 + \frac{x}{l} \right) \hat k$. $A$ square loop of edge $l$ and carrying a current $i$ is placed with its edges parallel to $x-y$ axes. Find the magnitude of the net magnetic force experienced by the loop.

$A$ straight horizontal long wire carries $30 \ A$ current. The linear mass density of the wire is $45 \ g/m$. What is the magnitude of the magnetic field needed to balance the wire in air?

$A$ 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:

$A$ straight horizontal conducting rod of length $0.45\; m$ and mass $60\; g$ is suspended by two vertical wires at its ends. $A$ current of $5.0\; A$ is set up in the rod through the wires.
$(a)$ What magnetic field should be set up normal to the conductor in order that the tension in the wires is zero?
$(b)$ What will be the total tension in the wires if the direction of current is reversed keeping the magnetic field same as before? (Ignore the mass of the wires.) $g = 9.8\; m s^{-2}.$

$A$ thin flexible wire of length $L$ is connected to two adjacent fixed points and carries a current $I$ in the clockwise direction,as shown in the figure. When the system is put in a uniform magnetic field of strength $B$ going into the plane of the paper,the wire takes the shape of a circle. The tension in the wire is

$A$ square coil $ABCD$ of side $L$ is carrying a current $I_1$ in the clockwise direction. $A$ straight conductor carrying current $I_2$ (upward direction) is kept parallel to side $AB$ at a distance $\frac{L}{3}$ in the plane of $ABCD$. The net force on the coil $ABCD$ is ($\mu_0 =$ magnetic permeability).