A steady current I goes through a wire loop PQR having the shape of a right-angled triangle with PQ = 3x, PR = 4x, and QR = 5x. If the magnitude of the magnetic field at P due to this loop is k(μ₀I/48πx), find the value of k.

Magnetic field at P due to side PQ and RP are zero respectively since point P is on the sides PQ and RP. From the diagram, in ΔPQS and ΔPSR, the sum of all the angles of a triangle are 180°; ∠QPS = 37°; ∠SPR = 53° since ∠PRQ = ∠PSR = 90° PS = PQsin53° = 3x × 4/5 = 12x/5
Magnetic field at P due to side QR:
→B = μ₀i/4πPS(sin53° + sin37°) = μ₀i/4π × 12x/5 (4/5 + 3/5) = 7μ₀i/48πx
∴k = 7