$A$ rigid wire consists of a semicircular portion of radius $R$ and two straight sections. The wire is partially immersed in a perpendicular magnetic field $B = B_0 \hat{k}$ as shown in the figure. The magnetic force on the wire if it carries a current $i$ is:

$A$ 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.

$A$ wire $AB$ is carrying a steady current $I_1$ and is kept on a table. Another wire $CD$ carrying current $I_2$ is held directly above it at a distance $r$. When the wire $CD$ is left free and it remains suspended at its position, find its mass per unit length. (Given: $g$ = acceleration due to gravity, $\mu_0$ = permeability of free space)

$A$ rectangular coil $ABCD$ is hung from one side of a balance as shown in the figure. $A$ $500 \, g$ mass is added to the other arm to balance the weight of the coil. $A$ current of $9.8 \, A$ is passed through the coil and a constant magnetic field of $0.4 \, T$ acting inward is switched on such that only arm $CD$ of length $1.5 \, cm$ lies in the field. The additional mass $m$ that must be added to regain the balance is: (in $, g$)

The figure shows a conducting loop $ABCDA$ placed in a uniform magnetic field perpendicular to its plane. The part $ABC$ is the $(3/4)^{th}$ portion of the square of side length $l$. The part $ADC$ is a circular arc of radius $R$. The points $A$ and $C$ are connected to a battery which supplies a current $I$ to the circuit. The magnetic force on the loop due to the field $B$ is

$A$ wire of length $L$ carries a current $I$ along the $X$-axis. The magnetic force acting on the wire is given by $\vec{F} = I B_0 L(\hat{k} - \hat{j})$. The existing magnetic field $\vec{B}$ is