Question

Considering the case of magnetic field produced by air-filled current carrying solenoid, show that the magnetic energy density of a magnetic field B is `B^2/(2mu_0)`.

Answer 1

Let the permittivity, permeability of free space, electric field, velocity of light are ε₀, μ₀, E, c respectively. The permittivity is given as:

ε₀ = `1/(c^2mu_0)`

The electric field is given as: E = Bc

The energy stored in a capacitor per unit volume is:

`u/(AI) = 1/2 epsilon_0E^2`

u = `1/2 xx 1/(c^2mu_0) xx (Bc)^2 xx Al`

The magnetic energy density u = `u/(Al) = B^2/(2mu_0)`