Scott Hughes
24 February 2004
Massachusetts Institute of Technology
Department of Physics
8.022 Spring 2004
Lecture 6:
Capacitance
6.1
Capacitance
Suppose that I have two chunks of metal. A charge +
Q
is on one of these chunks,

Q
is
on the other (so that the system is neutral overall). Each chunk will be at some constant
potential. What is the potential difference between the two chunks of metal?
+Q
Q
2
1
+
+
+
+
+
+






Whatever the potential difference
V
≡
φ
2

φ
1
=

R
2
1
~
E
·
d~s
turns out to be, it must of
course turns out to be independent of the integration path. In fact, as we can show with a
little thought, the potential difference
V
must be proportional to the geometry. This means
that the potential difference (or “voltage”) between the two chunks must take the form
V
= (Horribly messy constant depending on geometry)
×
Q .
The horrible mess that appears in this proportionality law depends only on geometry. In
other words, it will depend on the size and shape of the two metal chunks, their relative
orientation, and their separation. It does
not
depend on their charge.
This constant is defined as 1
/C
, where
C
is the
Capacitance
of this system. A system like
this is then called a
capacitor
. The 1
/
may seem a bit wierd; the point is that one usually
writes the capacitance formula in a different way: we put
Q
=
CV .
A key thing to bear in mind when using this formula is that
Q
refers to the charge
separation
of the system. In other words, when I say that a capacitor is charged up to some level
Q
,
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Figure 1:
Q
=
CV
.
I mean that I have put +
Q
on one part of the capacitor,

Q
on the other.
The capacitor
as a whole remains neutral!!
I emphasize this now because I often find students are some
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 Spring '08
 Hughes
 Capacitance, Charge, Mass, Potential difference, Electric charge, Farad

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