Maxwell’s equations relating the electric field E and magnetic field H as they vary with time in a region containing no charge and no current can be stated as follows: div E = 0 div H = 0 curt E = − 1 c ∂ H ∂ t curl H = 1 c ∂ E ∂ t where c is the speed of light. Use these equations to prove the following: (a) ∇ × ( ∇ × E ) = − 1 c 2 ∂ 2 E ∂ t 2 (b) ∇ × ( ∇ × H ) = − 1 c 2 ∂ 2 H ∂ t 2 (c) ∇ 2 E = 1 c 2 ∂ 2 E ∂ t 2 [ Hint: Use Exercise 29.] (d) ∇ 2 H = 1 c 2 ∂ 2 H ∂ t 2
Maxwell’s equations relating the electric field E and magnetic field H as they vary with time in a region containing no charge and no current can be stated as follows: div E = 0 div H = 0 curt E = − 1 c ∂ H ∂ t curl H = 1 c ∂ E ∂ t where c is the speed of light. Use these equations to prove the following: (a) ∇ × ( ∇ × E ) = − 1 c 2 ∂ 2 E ∂ t 2 (b) ∇ × ( ∇ × H ) = − 1 c 2 ∂ 2 H ∂ t 2 (c) ∇ 2 E = 1 c 2 ∂ 2 E ∂ t 2 [ Hint: Use Exercise 29.] (d) ∇ 2 H = 1 c 2 ∂ 2 H ∂ t 2
Maxwell’s equations relating the electric field E and magnetic field H as they vary with time in a region containing no charge and no current can be stated as follows:
div
E
= 0
div
H
= 0
curt
E
=
−
1
c
∂
H
∂
t
curl
H
=
1
c
∂
E
∂
t
where c is the speed of light. Use these equations to prove the following:
(a)
∇
×
(
∇
×
E
)
=
−
1
c
2
∂
2
E
∂
t
2
(b)
∇
×
(
∇
×
H
)
=
−
1
c
2
∂
2
H
∂
t
2
(c)
∇
2
E
=
1
c
2
∂
2
E
∂
t
2
[Hint: Use Exercise 29.]
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