JEE Main 2025 Apr 2 Shift 2, Physics Q8: Magnetic Flux

JEE Main2025Apr 2, Shift 2Physics

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
$\frac{B ^{2} A l}{4 μ _{0}}$

Solution

Energy density of a magnetic field in a linear medium of permeability $μ = μ_{r} μ_{0}$ is

$u = \frac{B ^{2}}{2 μ} = \frac{B ^{2}}{2 μ _{r} μ _{0}}$ .

With $μ_{r} = 2$ : $u = \frac{B ^{2}}{4 μ _{0}}$ .

Total energy stored in the solenoid volume $V = A l$ :

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

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JEE Main 2025 Apr 2 Shift 2, Physics Q8: Magnetic Flux

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