$A$ 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.

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.

$A$ 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 $\,N$)?

$A$ rectangular loop carrying a current $i$ is situated near a long straight wire such that the wire is parallel to one of the sides of the loop and is in the plane of the loop. If a steady current $i$ is established in the wire as shown in the figure,the loop will

Two parallel wires of length $9 \, m$ each are separated by a distance $0.15 \, m$. If they carry equal currents in the same direction and exert a total force of $30 \times 10^{-7} \, N$ on each other,then the value of current must be ........ $A$. (in $.5$)

$A$ $100$ 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?