Massachusetts Institute of Technology
Department of Physics
8.022 Spring 2004
Assignment 11: Poynting vector practice
Post date: Friday, May 7th
Due date:
NEVER
1. Poynting vector and capacitor: in this problem, you will finish the calculation that I
laid out in lecture. A current
I
=
dQ/dt
delivers charge to a capacitor. This capacitor
has radius
a
, and the plates are separated by a distance
s
.
a
+Q
Q
I
s
First, for practice with these concepts, redo the bits that I did in lecture:
(a) Calculate the electric field — magnitude and direction — between the plates.
(b) Calculate the magnetic field — magnitude and direction — induced by as the
electric field changes with time.
(c) Calculate the Poynting vector due to this
~
E
and
~
B
. Verify that it points into the
capacitor.
Now, finish the calculation:
(d) Calculate the total power,
P
=
R
~
S
·
d~a
, flowing into the capacitor.
Given the
Poynting vector you worked out in (c), what is the correct surface to use for the
integral?
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 Spring '08
 Hughes
 Solar System, Energy, Mass, Coaxial cable, Poynting vector

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