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.

Wires $1$ and $2$ carrying currents $i_1$ and $i_2$ respectively are inclined at an angle $\theta$ to each other. What is the force on a small element $dl$ of wire $2$ at a distance of $r$ from wire $1$ (as shown in figure) due to the magnetic field of wire $1$?

$A$ $100$ turn rectangular coil $ABCD$ (in $xy$-plane) is hung from one arm of a balance (Figure). $A$ mass of $500 \text{ g}$ is added to the other arm to balance the weight of the coil. $A$ current of $4.9 \text{ A}$ passes through the coil and a constant magnetic field of $0.2 \text{ T}$ acting inward (in $xz$-plane) is switched on such that only arm $CD$ of length $1 \text{ cm}$ lies in the field. How much additional mass '$m$' must be added to regain the balance?

$A$ 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 $\,N$)?

Two thin long parallel wires separated by a distance $b$ are carrying a current $i$ $A$ each. The magnitude of the force per unit length exerted by one wire on the other is

$A$ wire is bent as a parabolic curve and kept in the $x-y$ plane. The curve is described by the equation $x^2 = 6y$. The wire carries a current $i = 2 \ A$. If a uniform magnetic field $\vec{B} = 2 \times 10^{-3} \hat{k} \ T$ is applied,the force experienced by the wire is nearly: (in $hat{j} \ N$)