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Introduction to Electrodynamics
· Problem 7.37
Conservation Laws — David J. Griffiths
Physics · maxwells-equations
Problem
Suppose
E
(
r
,
t
)
=
1
4
π
ϵ
0
q
r
2
θ
(
v
t
−
r
)
r
^
;
B
(
r
,
t
)
=
0
\mathbf{E}(\mathbf{r}, t) = \frac{1}{4\pi\epsilon_0} \frac{q}{r^2} \theta(vt - r)\hat{r}; \quad \mathbf{B}(\mathbf{r}, t) = \mathbf{0}
E
(
r
,
t
)
=
4
π
ϵ
0
1
r
2
q
θ
(
v
t
−
r
)
r
^
;
B
(
r
,
t
)
=
0
(The theta function is defined in Prob. 1.46b). Show that these fields satisfy all of Maxwell's equations, and determine
ρ
\rho
ρ
and
J
\mathbf{J}
J
. Describe the physical situation that gives rise to these fields.
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