A square loop ABCD of side L carries current i and lies in the plane of a long straight conductor XY carrying current I. The nearest loop side is at distance L/2 from the wire, as shown. Find the magnitude of the net magnetic force on the loop. [Image]
Options

Question

A square loop ABCD of side L carries current i and lies in the plane of a long straight conductor XY carrying current I. The nearest loop side is at distance L/2 from the wire, as shown. Find the magnitude of the net magnetic force on the loop. [Image]

Options

G1 Physics · Accepted Answer

Step 1: Force between two long parallel current elements along common length L separated by r is F = μ₀IiL/(2πr). Step 2: For the nearest vertical side of the square, r₁=L/2, so F₁ = μ₀Ii/π. For the far side, r₂=3L/2, so F₂ = μ₀Ii/(3π). Step 3: These vertical-side forces oppose, while horizontal-side contributions cancel by symmetry. Step 4: Magnitude of net force: F = F₁−F₂ = (2μ₀Ii)/(3π). Final answer: (D) 2μ₀Ii/(3π).