A horizontal wire $AB$ of length $\text{'}I\text{'}$ and mass $\text{'}m\text{'}$ carries a steady current $I_1$, free to move in vertical plane is in equilibrium at a height of $\text{'}h\text{'}$ over another parallel long wire $CD$ carrying a steady current $I_2$, which is fixed in a horizontal plane as shown. Derive the expression for the force acting per unit length on the wire $AB$ and write the condition for which wire $AB$ is in equilibrium.

Figure shows three infinitely long straight parallel current carrying conductors. Find the
(i) magnitude and direction of the net magnetic field at point $A$ lying on conductor $1$.

Figure shows three infinitely long straight parallel current carrying conductors. Find the (ii) magnetic force on conductor $2$.

In Figure, the straight wire $AB$ is fixed while the loop $PQRS$ is free to move under the influence of the electric currents flowing in them. In which direction does the loop begin to move ? Give reason for your answer.

Write the expression for the magnetic moment $\left(\overrightarrow{m}\right)$ due to a planar square loop of side $\text{'}l\text{'}$ carrying a steady current $I$ in a vector form. As shown in Figure, this
loop is placed in a horizontal plane near a long straight conductor carrying a steady current $I_1$ at a distance $l$. Give reasons to explain that the loop will experience a net force but no torque. Write the expression for this force acting on the loop.