A solenoid of cross-sectional area A and length l is filled with a material of relative permeability 2. If the magnetic field inside the solenoid is B, the magnetic energy stored in the solenoid is:
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Question

A solenoid of cross-sectional area A and length l is filled with a material of relative permeability 2. If the magnetic field inside the solenoid is B, the magnetic energy stored in the solenoid is:

G1 Physics · Accepted Answer

The magnetic energy density in a material of permeability μ is u = B²/(2μ). Here the relative permeability is μᵣ = 2, so μ = μᵣμ₀ = 2μ₀. Therefore, u = B²/[2(2μ₀)] = B²/(4μ₀). The volume of the solenoid is V = Al. Hence total magnetic energy is U = uV = [B²/(4μ₀)]Al = B²Al/(4μ₀). Correct option: A.