Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Introduction to Electrodynamics
· Problem 10.26
Potentials and Fields — David J. Griffiths
Physics · retarded-potentials
Problem
An expanding sphere, radius
R
(
t
)
=
v
t
R(t) = vt
R
(
t
)
=
v
t
(
t
>
0
t > 0
t
>
0
, constant
v
v
v
) carries a charge
Q
Q
Q
, uniformly distributed over its volume. Evaluate the integral
Q
eff
=
∫
ρ
(
r
,
t
r
)
d
τ
Q_{\text{eff}} = \int \rho(\mathbf{r}, t_r)\, d\tau
Q
eff
=
∫
ρ
(
r
,
t
r
)
d
τ
with respect to the center. Show that
Q
eff
≈
Q
(
1
−
3
v
4
c
)
Q_{\text{eff}} \approx Q(1 - \frac{3v}{4c})
Q
eff
≈
Q
(
1
−
4
c
3
v
)
, if
v
≪
c
v \ll c
v
≪
c
.
Related theory
retarded-potentials
Browse the problem library