A long solenoid has length ℓ, radius r, and n turns per unit length. If μ₀ is the permeability of free space, what is its self-inductance?
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Question

A long solenoid has length ℓ, radius r, and n turns per unit length. If μ₀ is the permeability of free space, what is its self-inductance?

G1 Physics · Accepted Answer

Step 1: Total number of turns N = nℓ and area of each turn A = πr². Step 2: Magnetic field well inside the long solenoid is B = μ₀nI. Step 3: Flux linkage is NΦ = N(BA) = (nℓ)(μ₀nI)(πr²). Step 4: By definition L = NΦ/I = μ₀πn²r²ℓ. Final answer: μ₀πn²r²ℓ (Option A).