Energy Density Formula

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

UE = εE2/2

In the case of magnetic energy

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

The equation is written

UB = B2/2*μ

The general energy is:

U = UE + UB

We have:

U = energy density

UE = electrical energy density

UB = 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*10-3T, and the electric field has a value of 3*106V/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*10-3T, E = 3*106V/m, ε = 8.85*10-12C2/N*m2 and μ = 4π*10-7N/A2.

UE = εE2/2

UE = 8.85*10-12C2/N·m2*(3*106V/m)2/2

UE = 39.825J/m3

UB = B2/2*μ

UB = (5*10-3T)2/2*4π*10-7N/A2

UB = 9.95J/m3

U = UE+UB

U = 39.825J/m3+9.95J/m3

U = 49.775J/m3.

2) In a certain region of space, the magnetic field has a value of 3*10-2T, and the electric field has a value of 9*107V/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*10-2T, E = 9*107V/m, ε = 8.85*10-12C2/N*m2 and μ = 4π*10-7N/A2.

UE = εE2/2

UE = 8.85*10-12C2/N·m2*(9*107V/m)2/2

UE = 35842.5J/m3

UB = B2/2*μ

UB = (3*10-2T)2/2*4π*10-7N/A2

UB = 358.1J/m3

U = UE+UB

U = 35,842.5J/m3+358.1J/m3

U = 36200.6J/m3

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