$A$ massless square loop of wire of resistance $R$ supporting a mass $M$ hangs vertically with one of its sides in a uniform magnetic field $B$ directed outwards in the shaded region. $A$ d.c. voltage $V$ is applied to the loop. For what value of $V$ will the magnetic force exactly balance the weight of the supporting mass $M$? (side of loop $= L, g =$ acceleration due to gravity)

$A$ 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.) $g = 9.8\; m s^{-2}.$

$A$ horizontal metallic rod of mass $m$ and length $l$ is supported by two vertical identical springs of spring constant $K$ each and natural length $l_0$. $A$ current $i$ is flowing in the rod in the direction shown. If the rod is in equilibrium,then the length of each spring in this state is:

Three long straight wires $A$,$B$,and $C$ are carrying currents as shown in the figure. Then the resultant force on $B$ is directed .....

$A$ horizontal wire carries $160 \ A$ current. Below it, another wire with a linear mass density of $10 \ g \ m^{-1}$ is kept at a distance of $4 \ cm$. If the lower wire hangs in the air, what is the current in this wire when the direction of current in both wires is the same (in $A$)? $(g=10 \ m \ s^{-2} \text{ and } \mu_0=4 \pi \times 10^{-7} \ T \ m \ A^{-1})$

$A$ semi-circular loop of radius $30 \,cm$ wire carries current $6 \,A$. $A$ uniform magnetic field $0.5 \,T$ is present perpendicular to the plane of the loop. What is the magnitude of force exerted on the wire (in $\,N$)?