Two parallel conductors carrying unequal currents in the same direction . . . . . .

The horizontal component of the earth's magnetic field at a certain place is $3.0 \times 10^{-5} \; T$ and the direction of the field is from the geographic south to the geographic north. $A$ very long straight conductor is carrying a steady current of $1 \; A$. What is the force per unit length on it when it is placed on a horizontal table and the direction of the current is $(a)$ east to west; $(b)$ south to north?

The force per unit length on a straight wire carrying a current of $8 \ A$ making an angle of $30^{\circ}$ with a uniform magnetic field of $0.15 \ T$ is: (in $N \ m^{-1}$)

Two wires $A$ and $B$ are carrying currents $I_1$ and $I_2$ as shown in the figure. The separation between them is $d$. $A$ third wire $C$ carrying a current $I$ is to be kept parallel to them at a distance $x$ from $A$ such that the net force acting on it is zero. The possible values of $x$ are

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.

$A$ massless square loop of wire of resistance $R$ supporting a mass $M$ hangs vertically with one of its sides in a uniform magnetic field $B$ directed outwards in the shaded region. $A$ d.c. voltage $V$ is applied to the loop. For what value of $V$ will the magnetic force exactly balance the weight of the supporting mass $M$? (side of loop $= L, g =$ acceleration due to gravity)