The electric and magnetic fields have energy and hence have an energy density.
We can see this for a capacitor:The energy stored in a capacitor is
U
=
1
2
C
V
2
U
=
1
2
C
V
2
where
C
C
is the capacitance and
V
V
the potential drop (voltage) across the capacitor. For a parallel plate
capacitor
C
=
ε
0
A
d
C
=
ε
0
A
d
and
V
=
E
d
V
=
E
d
where
A
A
is the area of the plates
d
d
the distance between them and
E
E
the electric field strength.note that
A
d
A
d
is the volumeThus
U
=
1
2
ε
0
A
d
(
E
d
)
2
=
1
2
ε
0
A
d
E
2
U
=
1
2
ε
0
A
d
(
E
d
)
2
=
1
2
ε
0
A
d
E
2
So we can write the energy density (Energy per Unit volume) of the field as
u
E
=
U
A
d
=
1
2
ε
0
E
2
u
E
=
U
A
d
=
1
2
ε
0
E
2
Likewise by calculating the energy stored by a B-field in a current
carrying solenoid one can derive:
u
B
=
B
2
2
μ
0
u
B
=
B
2
2
μ
0
Since we know
E
=
c
B
E
=
c
B
u
E
=
1
2
ε
0
E
2
=
1
2
ε
0
c
2
B
2
=
1
2
ε
0
1
ε
0
μ
0
B
2
=
1
2
1
μ
0
B
2
=
u
B
u
E
=
1
2
ε
0
E
2
=
1
2
ε
0
c
2
B
2
=
1
2
ε
0
1
ε
0
μ
0
B
2
=
1
2
1
μ
0
B
2
=
u
B
In an EM wave
u
=
u
E
+
u
B
u
=
u
E
+
u
B
which is
u
=
ε
0
E
2
u
=
ε
0
E
2
or equivalently
u
=
B
2
/
μ
0
u
=
B
2
/
μ
0