Physics Q43 – JEE-MAIN 2025

Home Physics Magnetism and MatterQuestion #246

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 :

Clue 1 of 3: Magnetic Energy Storage

Recall the formula for magnetic energy density in a medium and how it relates to the magnetic field and permeability.

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Ninja Strategy•Permeability Factor Analysis

Recognize that the energy density formula $U = \frac{B^{2}}{2 μ} V$ means that a higher permeability (like $μ_{r} = 2$ ) should lead to a smaller stored energy for the same B field, thus increasing the denominator by a factor of $μ_{r}$ compared to vacuum.

🧠 Full Solution Path

Step 1: Determine the permeability of the medium✦ Active

The solenoid is filled with a material having relative permeability $μ_{r} = 2$ . The absolute permeability of the material is given by $μ = μ_{r} μ_{0}$ .

μ = 2 μ_{0}

Step 2: Calculate the magnetic energy density○ Expand

The magnetic energy density $u$ stored in a magnetic field $B$ within a medium of permeability $μ$ is given by $u = \frac{B^{2}}{2 μ}$ . Substitute the value of $μ$ .

u = \frac{B^{2}}{2 (2 μ_{0})} = \frac{B^{2}}{4 μ_{0}}

Step 3: Calculate the total magnetic energy○ Expand

The volume of the solenoid is $V = A l$ . The total magnetic energy $U$ stored in the solenoid is the product of the energy density and the volume.

U = u \times V = (\frac{B^{2}}{4 μ_{0}}) (A l) = \frac{B^{2} A l}{4 μ_{0}}

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Physics Question 43 – JEE-MAIN 2025

Clue 1 of 3: Magnetic Energy Storage

🧠 Full Solution Path