Question

A current $I_1$ carrying wire AB is placed near another long wire CD carrying current $I_2$. If wire AB is free to moves, it will have:

• A. rotational motion only
• B. translational motion only
• C. rotational as well as translational motion
• D. neither rotational nor translational motion

Answer 1

The correct option is C rotational as well as translational motion

The magnetic field around the wire CD at a distance $r$ from it = $\frac{{\mu }_0{I}_2}{2\pi r}$

Thus the magnitude of magnetic field decreases along the wire AB due to wire CD.

On each small element of wire AB, force = $I_{1}Bdr$

Thus the force at each point is always in upward direction but decreases in magnitude as we go from nearer end to wire CD to the farther end.

Thus the translation is due to all forces acting in upward direction and rotation is due to all forces being different in magnitudes.