If an electric field E exists at a point in free space then the energy density in that point is 1 2 ϵ 0 | E | 2 When a field with same magnitude | E | exists in a material with relative permettivity k, the energy density becomes 1 2 ϵ 0 k | E | 2 , i.e. it increases k times.A similar analysis for energy density in magnetic field 1 2 μ 0 | B | 2 states that: if the field B exists in a material with relative permeability k (consider a ferromagnetic material, for example) then μ = k μ 0 and thus the energy density decreases k times (?). But this does not seem right because inductors with ferromagnetic cores store more energy.

Question

If an electric field       E   exists at a point in free space then the energy density in that point is       1    2        ϵ    0        |        E              |        2  When a field with same magnitude       |        E        |   exists in a material with relative permettivity k, the energy density becomes       1    2        ϵ    0    k      |        E              |        2  , i.e. it increases k times.A similar analysis for energy density in magnetic field       1          2              μ        0                  |        B              |        2   states that: if the field       B   exists in a material with relative permeability k (consider a ferromagnetic material, for example) then   μ  =  k      μ    0   and thus the energy density decreases k times (?). But this does not seem right because inductors with ferromagnetic cores store more energy.

Carolyn Farmer · Accepted Answer

Inside a dielectric, an externally-applied electric field is reduced. Therefore, a higher energy density is required to generate a given electric field inside the dielectric. This means that for a given electric field inside a dielectric, the associated energy density will be larger than in the vacuum; intuitively, you have to &quot;work harder&quot; to produce an electric field in a dielectric, because a dielectric opposes the applied fields.Inside a ferromagnet, an externally-applied magnetic field is amplified. Therefore, a lower energy density is required to generate a given magnetic field inside the ferromagnet. This means that for a given magnetic field inside a ferromagnet, the associated energy density will be smaller than in the vacuum; intuitively, you &quot;don&#039;t have to work as hard&quot; to produce a magnetic field in a ferromagnet, because a ferromagnet amplifies the applied fields.Along the same lines, ferroelectric materials, which have dielectric constants less than 1, amplify fields like ferromagnets, so the energy density of the electric field inside a ferroelectric material will be reduced relative to the vacuum. Likewise, diamagnetic materials, which have relative permeabilities less than 1, reduce fields like dielectrics, so the magnetic field inside a diamagnetic material will be increased relative to the vacuum.

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