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Force between current-carrying conductors
Concepts tested here
- Force on a loop near a straight wire
All Questions
2011 AIPMT-MAINS 1 question
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A square loop, carrying a steady current I, is placed in a horizontal plane near a long straight conductor carrying a steady current $I_1$ at a distance d from the conductor as shown in figure. The loop will experience
The field of the long wire, $B = \frac{\mu_0I_1}{2\pi r}$, decreases with distance r from the wire.
The two sides of the loop perpendicular to the wire carry opposite currents at the same set of distances, so the forces on them are equal and opposite and cancel.
In the figure, the side of the loop nearer to the wire carries current in the same direction as $I_1$; parallel currents attract, so this side is pulled towards the wire with force $\frac{\mu_0I_1Il}{2\pi d}$.
The far side carries current in the opposite direction and is repelled, but it is at a larger distance (d + l), so this force is smaller.
The net force is therefore towards the wire; all forces lie in the plane of the loop and act along the same line, so there is no net torque.
Hence the loop experiences a net attractive force towards the conductor.