A square loop, carrying a steady current I, is placed in a horizontal plane near a long straight conductor carrying a steady current I₁, at a distance d from the conductor as shown in the figure. The loop will experience

Question

Accepted Answer

(1) a net attractive force towards the conductor. Given: the loop lies in the same plane as the wire, its near side at distance d and its far side at d+L; the figure shows the near side carrying current in the same direction as I₁. Idea: the two sides parallel to the wire feel opposite forces, and the field falls as 1/d, so the nearer one wins. Near side: current parallel to I₁, so it is attracted, with force (μ₀I₁IL)/(2π d). Far side: current antiparallel, so it is repelled, with force (μ₀I₁IL)/(2π(d+L)). The two sides perpendicular to the wire feel equal and opposite forces that cancel. Since d<d+L, the attraction on the near side is the larger. So the loop feels a net attraction towards the conductor.

A square loop, carrying a steady current I, is placed in a horizontal plane near a long straight conductor carrying a steady current I₁, at a distance d from the conductor as shown in the figure. The loop will experience

Step-by-step solution

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