A long flat current strip of width a carries current I uniformly. At point P in the plane of strip, at distance d from its nearest edge, B = (μ₀I)/(kπa) ln((d+a)/d). Find k. [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

A long flat current strip of width a carries current I uniformly. At point P in the plane of strip, at distance d from its nearest edge, B = (μ₀I)/(kπa) ln((d+a)/d). Find k. [See Image.]

G1 Physics · Accepted Answer

Step 1 — Uniform sheet current per unit width K=I/a. An infinitesimal strip of width dx carries dI=(I/a)dx. Step 2 — Field from a long straight filament at distance d+x is dB = μ₀ dI/[2π(d+x)]. Step 3 — Integrate from x=0 to a: B = μ₀I/(2πa) ln[(d+a)/d]. Step 4 — Compare with source B=μ₀I/(kπa) ln[(d+a)/d]. Therefore k=2.