Current density in an infinitely long circular conductor varies as j = brᵅ. Inside the conductor, the magnetic field has the form B = μ₀br⁽ᵅ⁺ˣ⁾/(α + y). Find x + y.
Physics · Mixed Chapter
JEE Main Practice

Question

Current density in an infinitely long circular conductor varies as j = brᵅ. Inside the conductor, the magnetic field has the form B = μ₀br⁽ᵅ⁺ˣ⁾/(α + y). Find x + y.

G1 Physics · Accepted Answer

Step 1 — For current density j(r) = brᵅ, current enclosed within radius r is Iₑₙc = ∫₀ʳ br′ᵅ(2πr′dr′) = 2πb r⁽ᵅ⁺²⁾/(α + 2). Step 2 — Ampère’s law B(2πr) = μ₀Iₑₙc. Step 3 — Hence B = μ₀ b r⁽ᵅ⁺¹⁾/(α + 2). Compare with μ₀br⁽ᵅ⁺ˣ⁾/(α + y): x = 1, y = 2. Step 4 — x + y = 3.