A straight wire carrying 20 A passes near a rectangular loop (height 20 cm, width 15 cm, nearer edge 5 cm from the wire). When the wire current falls to zero, the total induced charge through the 20 Ω loop is k×10⁻⁸ ln 2 coulomb. Find k.
Physics · Mixed Chapter
JEE Mains

Question

A straight wire carrying 20 A passes near a rectangular loop (height 20 cm, width 15 cm, nearer edge 5 cm from the wire). When the wire current falls to zero, the total induced charge through the 20 Ω loop is k×10⁻⁸ ln 2 coulomb. Find k.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — Magnetic field of the long straight conductor: At distance x from a straight current-carrying wire, B(x) = μ₀I/(2πx). Step 2 — Flux through the neighbouring rectangular loop: The loop height is h = 0.20 m. The nearest and farthest distances from the wire are a = 0.05 m and b = 0.05 + 0.15 = 0.20 m. Φ = ∫ₐᵇ B(x)h dx = (μ₀Ih/2π)ln(b/a). Step 3 — Total charge passing during current decay: From Faraday's law and Ohm's law, |Δq| = |ΔΦ|/R. With ΔI = 20 A and loop resistance R = 20 Ω: |Δq| =…