Energy density is denoted by the letter U.
Magnetic and electric fields can also store energy.
In the case of an electric field or capacitor, the energy density is given by UE =
1212εoE2
The energy density in the case of magnetic field or inductor is given by, UB =
12μ012�0 B2
Where UE = Electrical energy density
UB= Magnetic energy density
εo=Permittivity
E= Electric field
B=Magnetic field
μ= magnetic permeability
For electromagnetic waves, both magnetic and electric fields are equally involved in contributing to energy density. Therefore, the energy density is the sum of the energy density of electric and magnetic fields.
i.e., U =
1212εoE2 +
12μ012�0B2
Solved Examples
Example 1: In a certain region of space, the magnetic field has a value of 1.0 × 10–2 T, and the electric field has a value of 2.0 ×106 Vm-1. Find the combined energy density of the electric and magnetic fields.
Solution: E = 2.0 × 106 Vm-1; B = 1.0 × 10-2 T
For the electric field, the energy density is UE =
1212 εoE2
=12 × 8.85 × 10−12(2.0 × 106)2 = 18Jm−3
For the magnetic field, the energy density is UB =
12μ012�0B2
=
12×(1.0×10−2)24π×10−7=40jm−312×(1.0×10−2)24�×10−7=40��−3
The net energy density is the sum of the energy density due to the electric field and the energy density due to the magnetic field:
U= UE + UB = 18 + 40 = 58 Jm-3
Example 2: In a certain region of space, the magnetic field has a value of 3X10-2T, and the electric field has a value of 9X107 V/m. Calculate the energy density of the electric and magnetic fields?
Solution: B = 3 X 10-2T, E = 9 X 107 V/m, ε = 8.85 X 10-12 C2 / Nm2 and μ = 4π X 10-7 N/A2.
UE = 12εoE2
UE = 8.85 X 10-12 C2 / Nm2 X (9X107V/m)2/2
UE = 35842.5 J/m3
UB =12μ0B2
UB = (3 X 10-2T)2 / 2 X 4π X 10-7 N/A2
UB = 358.1J/m3
U = UE + UB
U = 35,842.5 J/m3 + 358.1 J/m3
U = 36200.6 J/m3
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