Two identical long ideal solenoids meet end-to-end, each of area A with n turns per unit length. Currents are I₁ and I₂. If axial magnetic force is μ₀I₁I₂n²A/N, determine N. [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

Two identical long ideal solenoids meet end-to-end, each of area A with n turns per unit length. Currents are I₁ and I₂. If axial magnetic force is μ₀I₁I₂n²A/N, determine N. [See Image.]

G1 Physics · Accepted Answer

Step 1 — On-axis field from long ideal solenoid 1 is B₁ = μ₀ nI₁ inside and approximately B₁/2 at its open end. Step 2 — Solenoid 2’s end behaves as an effective magnetic pole of strength mₚ = nI₂A in the field of first solenoid. Step 3 — Force F = mₚ × (B₁/2) = μ₀ I₁I₂n²A/2. Step 4 — Thus N = 2.