# Energy Density Formula

Energy density is defined as the amount of energy accumulated in a system per unit volume.

In the case of electrical energy

Electrical energy density = permittivity* Electric field squared/2

The equation is written

U_{E} = εE^{2}/2

In the case of magnetic energy

Magnetic energy density = magnetic field squared/ 2* magnetic permeability

The equation is written

U_{B} = B^{2}/2*μ

The general energy is:

U = U_{E} + U_{B}

We have:

U = energy density

U_{E} = electrical energy density

U_{B} = magnetic energy density

ε = permittivity

E = Electric field

B = Magnetic field

μ = magnetic permeability

Energy density Questions:

1) In a certain region of space, the magnetic field has a value of 5*10^{-3}T, and the electric field has a value of 3*10^{6}V/m. What is the combined energy density of the electric and magnetic fields?

Answer: First we calculate the density and energy of each field, finally we add the densities to obtain the total energy density, where B = 5*10^{-3}T, E = 3*10^{6}V/m, ε = 8.85*10^{-12}C^{2}/N*m^{2} and μ = 4π*10^{-7}N/A^{2}.

U_{E} = εE^{2}/2

U_{E} = 8.85*10^{-12}C^{2}/N·m^{2}*(3*10^{6}V/m)^{2}/2

U_{E} = 39.825J/m^{3}

U_{B} = B^{2}/2*μ

U_{B} = (5*10^{-3}T)^{2}/2*4π*10^{-7}N/A^{2}

U_{B} = 9.95J/m^{3}

U = U_{E}+U_{B}

U = 39.825J/m^{3}+9.95J/m^{3}

U = 49.775J/m^{3}.

2) In a certain region of space, the magnetic field has a value of 3*10^{-2}T, and the electric field has a value of 9*10^{7}V/m. What is the combined energy density of the electric and magnetic fields?

Answer: First we calculate the density and energy of each field, finally we add the densities to obtain the total energy density, where B = 3*10^{-2}T, E = 9*10^{7}V/m, ε = 8.85*10^{-12}C^{2}/N*m^{2} and μ = 4π*10^{-7}N/A^{2}.

U_{E} = εE^{2}/2

U_{E} = 8.85*10^{-12}C^{2}/N·m^{2}*(9*10^{7}V/m)^{2}/2

U_{E} = 35842.5J/m^{3}

U_{B} = B^{2}/2*μ

U_{B} = (3*10^{-2}T)^{2}/2*4π*10^{-7}N/A^{2}

U_{B} = 358.1J/m^{3}

U = U_{E}+U_{B}

U = 35,842.5J/m^{3}+358.1J/m^{3}

U = 36200.6J/m^{3}

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