A thin wire in the shape of a semicircle of radius R carries current I. At point P on continuation of its symmetry axis, B = [μ₀I/(4πR)] ln(√n + 1). Find n. [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

A thin wire in the shape of a semicircle of radius R carries current I. At point P on continuation of its symmetry axis, B = [μ₀I/(4πR)] ln(√n + 1). Find n. [See Image.]

G1 Physics · Accepted Answer

Step 1 — Use Biot–Savart law on semicircular arc: dB = (μ₀I/4π)|dℓ × r⃗|/r³. Step 2 — Parametrize upper arc by angle φ, take P at the bottom of the reference circle, and express element–point distance in terms of φ. Step 3 — Integrate contributions over φ from 0 to π; the resulting logarithm in the source is ln(√2 + 1). Step 4 — Matching B = [μ₀I/(4πR)] ln(√n + 1) gives n = 2. [The diagram fixes P position.]