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

Write the magnetic force equation on a current-carrying element $I\vec{dl}$ inside a magnetic field $\vec{B}$. Write the law used to determine the direction of the magnetic force.

Three long straight wires are connected in parallel to each other across a battery of negligible internal resistance. The ratio of their resistances is $3 : 4 : 5$. What is the ratio of the distances of the middle wire from the others if the net force experienced by it is zero?

$A$ 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

$A$ straight horizontal conducting rod of length $0.45\; m$ and mass $60\; g$ is suspended by two vertical wires at its ends. $A$ current of $5.0\; A$ is set up in the rod through the wires.
$(a)$ What magnetic field should be set up normal to the conductor in order that the tension in the wires is zero?
$(b)$ What will be the total tension in the wires if the direction of current is reversed keeping the magnetic field same as before? (Ignore the mass of the wires.) $g = 9.8\; m s^{-2}.$

An infinitely long current-carrying wire and a small current-carrying loop are in the plane of the paper as shown. The radius of the loop is $a$ and the distance of its centre from the wire is $d$ $(d >> a)$. If the loop applies a force $F$ on the wire,then: