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

$A$ and $B$ are two conductors carrying a current $i$ in the same direction. $x$ and $y$ are two electron beams moving in the same direction.

$A$ square loop $ABCD$ carries a current $i$ and is placed near a long straight wire $XY$ carrying a current $I$ as shown in the figure. What is the net force on the loop?

$A$ single turn current loop in the shape of a right-angled triangle with sides $5\,cm$,$12\,cm$,and $13\,cm$ carries a current of $2\,A$. The loop is placed in a uniform magnetic field of magnitude $0.75\,T$,whose direction is parallel to the current in the $13\,cm$ side of the loop. The magnitude of the magnetic force on the $5\,cm$ side is $\frac{x}{130}\,N$. The value of $x$ is $..........$

Two long straight wires are arranged parallel to each other and are kept $20$ cm apart in vacuum. They carry currents of $2$ $A$ and $4$ $A$ respectively in the same direction. What will be the magnetic force on a length of $10$ cm of either wire? $(\mu_0 = 4\pi \times 10^{-7} \text{ SI units})$

$A$ current of $10 \text{ A}$ flows through a horizontal straight wire $A$ with both ends rigidly fixed. Wire $B$ is placed directly above and parallel to $A$. The weight per unit length of wire $B$ is $40 \times 10^{-3} \text{ N/m}$ and it carries a current of $20 \text{ A}$. Find the distance of wire $B$ from wire $A$ so that wire $B$ remains at rest. Also,state the direction of current flowing through it.