An infinite straight wire carries i₁=1 A. A rectangular loop in the same plane carries i₂=1 A anticlockwise with dimensions as shown. If the net force magnitude is μ₀β/(4π), find β.

Question

G1 Physics · Accepted Answer

Only the two sides parallel to the long wire contribute net horizontal force; the transverse-side forces cancel. Using F/L=μ₀i₁i₂/(2πr) for the near and far sides and the shown distances gives F=μ₀/(4π), so β=1.