The horizontal component of earth's magnetic field at a place is $3.5 \times 10^{-5} \mathrm{~T}$. A very long straight conductor carrying current of $\sqrt{2} A$ in the direction from South east to North West is placed. The force per unit length experienced by the conductor is$..............$ $\times 10^{-6} \mathrm{~N} / \mathrm{m}$.

Two parallel conductors $A$ and $B$ of equal lengths carry currents $I$ and $10\, I$, respectively, in the same direction. Then

A circular conducting loop of radius $R$ carries a current $I.$ Another straight infinite conductor carrying current $I$ passes through the diameter of this loop as shown in the figure. The magnitude of force exerted by the straight conductor on the loop is

Consider the inferences given below in respect of the following current loop of wire kept is a magnetic field $\vec B$

$A.$ The force on the element $AC$ of the wire is $\frac{{\sqrt 3 }}{2}\,ILB$ directed into the page

$B.$ The force on the element $AB$ of the wire is $\frac{{\sqrt 3 }}{2}\,ILB$ directed into the page

$C.$ The total force on the loop $ABCA$ is zero.

Which of the above is /are not true ?

A thin flexible wire of length $\mathrm{L}$ is connected to two adjacent fixed points and carries a current $\mathrm{I}$ in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength $B$ going into the plane of the paper, the wire takes the shape of a circle. The tension in the wire is

There long straight wires $A$, $B$ and $C$ are carrying current as shown figure. Then the resultant force on $B$ is directed .....