$A, B$ and $C$ are three parallel conductors of equal lengths and carry currents $I, I$ and $2I$ respectively as shown in the figure. The distance between $A$ and $B$ and between $B$ and $C$ is $d$. If $F_1$ is the force exerted by $B$ on $A$ and $F_2$ is the force exerted by $C$ on $A$,then:

The force between two long parallel wires is $F$ when each one of them carries a certain current $I$. If the current in each is halved,the force between them would be . . . . . . .

$A$ straight rod of mass $m$ and length $L$ is suspended from two identical springs as shown in the figure. The springs are stretched by a distance of $x_0$ due to the weight of the rod. The circuit has a total resistance $R$. When a magnetic field perpendicular to the plane of the paper is switched on,the springs are observed to extend further by the same distance $x_0$. The magnetic field strength is:

$A$ square loop $ABCD$ of side length $L$ carrying a current $i$ is placed near and coplanar with a long straight conductor $XY$ carrying a current $I$. The distance between the wire $XY$ and the nearest side of the loop is $L/2$. The net force on the loop will be:

$A$ current loop $ABCD$ is held fixed on the plane of the paper as shown in the figure. The arcs $BC$ (radius $= b$) and $DA$ (radius $= a$) of the loop are joined by two straight wires $AB$ and $CD$. $A$ steady current $I$ is flowing in the loop. The angle made by $AB$ and $CD$ at the origin $O$ is $30^o$. Another straight thin wire with a steady current $I_1$ flowing out of the plane of the paper is kept at the origin. Due to the presence of the current $I_1$ at the origin:

$A$ uniform magnetic field of $1.5\; T$ exists in a cylindrical region of radius $10.0\; cm$,its direction parallel to the axis along east to west. $A$ wire carrying current of $7.0\; A$ in the north to south direction passes through this region. What is the magnitude and direction of the force on the wire if,
$(a)$ the wire intersects the axis,
$(b)$ the wire is turned from $N-S$ to northeast-northwest direction,
$(c)$ the wire in the $N-S$ direction is lowered from the axis by a distance of $6.0 \;cm?$