JEE Main · 2025 · 02 Apr 2025 · Shift 2 · Electromagnetic Induction

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A solenoid having area A and length 'l' is filled with a material having relative permeability 2. The magnetic energy stored in the solenoid is :

(A) $\frac{B ^{2} A l}{μ _{0}}$
(B) $\frac{B ^{2} A l}{2 μ _{0}}$
(C) $B^{2} A l$
(D) $\frac{B ^{2} A l}{4 μ _{0}}$ ✓ Correct

Answer: (D)

Solution

Energy density in a magnetic field is

u = \frac{B ^{2}}{2 μ}

, where

μ = μ_{r} μ_{0}

. With

μ_{r} = 2

, we have

u = \frac{B ^{2}}{2 \times 2 μ _{0}} = \frac{B ^{2}}{4 μ _{0}}

. Total energy stored:

U = u \times V = \frac{B ^{2}}{4 μ _{0}} \times A l = \frac{B ^{2} A l}{4 μ _{0}}

JEE Main · 2025 · 02 Apr 2025 · Shift 2 · Single correct option

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