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
|
Related Links: |