Three identical square loops made from one wire enclose time-varying magnetic field B = B₀t. Side of a square is a and wire resistance per unit length is λ. The induced current is written as B₀a/(4kλ). Find k. [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

Three identical square loops made from one wire enclose time-varying magnetic field B = B₀t. Side of a square is a and wire resistance per unit length is λ. The induced current is written as B₀a/(4kλ). Find k. [See Image.]

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — For a square loop, induced emf from uniform B(t) is ε = area × |dB/dt| = a²B₀. Step 2 — The three-loop wire creates multiple current paths, so assign branch currents and impose equal emf/voltage for shared segments. Step 3 — Each side has resistance λa; solve the current division for the specific 3-loop topology in the source figure. Step 4 — Comparing I = B₀a/(4kλ) with the result gives k = 3. [Image required.]