A coplanar circular loop of radius a = 3 m carries current I₂ and lies at distance b = 5 m (centre-to-wire) from an infinitely long straight wire carrying I₁. If interaction force has the form μ₀I₁I₂/n (as shown), find n. [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

A coplanar circular loop of radius a = 3 m carries current I₂ and lies at distance b = 5 m (centre-to-wire) from an infinitely long straight wire carrying I₁. If interaction force has the form μ₀I₁I₂/n (as shown), find n. [See Image.]

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — Field from long wire at distance x is B(x) = μ₀I₁/(2πx). Step 2 — Integrate magnetic force dF = I₂ dℓ × B over circular loop, accounting for different field strengths on near and far sides. Step 3 — The standard integral yields force magnitude F = μ₀I₁I₂ [b/√(b²−a²) − 1] for a circle of radius a at centre distance b. Step 4 — With a = 3 and b = 5, the bracket is 5/4 − 1 = 1/4. Thus F = μ₀I₁I₂/4 and n = 4.