A current carrying wire (current = i) perpendicular to the plane of the paper produces a magnetic field, as shown in the figure. A square of side a is drawn with one of its vertices on the centre of the wire. The integral . ∫B dr along OPQRO has the value

Question

G1 Physics · Accepted Answer

For the azimuthal field of a long straight wire, B=μ₀i/(2πr). Evaluating the line integral along the square path OPQRO gives one-quarter of μ₀i because the path subtends a net azimuthal angle π/2. Thus ∫B⃗·dr⃗=μ₀i/4, option C.