The magnetic field existing in a region is given by $\vec B = B_0 [1 + \frac{x}{l}] \hat k$. $A$ square loop of edge $l$ carrying current $I_0$ is placed with its edges parallel to the $x-y$ axes. Find the magnitude of the net magnetic force experienced by the loop.

$A$ 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)

$A$ current $I$ flows along the length of a thin-walled,long metallic hollow cylinder of radius $R$,distributed uniformly on its surface. The pressure on the wall will be:

As shown in the figure, a wire is bent to form a $D$-shaped loop carrying current $I$, where the curved part is a semi-circle of radius $R$. The loop is placed in a uniform magnetic field $\overrightarrow{B}$, which is directed into the plane of the paper. The net magnetic force on the closed loop is:

$A$ straight wire of mass $200 \;g$ and length $1.5 \;m$ carries a current of $2 \;A$. It is suspended in mid-air by a uniform horizontal magnetic field $B$ (Figure). What is the magnitude of the magnetic field (in $T$)?

An arrangement of three parallel wires placed perpendicular to the plane of the paper,each carrying the same current $I$ in the same direction,is shown in the figure. The magnitude of the force per unit length on the middle wire $B$ is given by: