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Capacitance
Electric fields can be used to store energy.
How?
Any two conductors
near each other form a
CAPACITOR, we saythere is capacitance in
the system
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Capacitance
A capacitor is an energy storage device.
A capacitor can store charge: q is
remoed from one side of the
capacitor and p!aced onto the other,
!eaing one side with "#q$ and the
other side with "%q$&
'e hae to do 'OR( to do this&
If we connect the two conductors
with a wire, the charges f!ow to ma)e
the potentia! difference *etweenconductors + &
'hen this happens, energy is
re!eased
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Capacitance
Analogy with air tank:
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Capacitance
Charge that can *e stored
in capacitor is proportiona!
to the potentia! "o!tage$
which is pushing the
charge into the conductors
Constant of proportiona!ity
is C, the capacitance
Definition of capacitance:
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Capacitance
C is just a function of geometry between two
conductors
-enera! method to ca!cu!ate capacitance:
a$ Assume a charge on the conductors
*$ Ca!cu!ate the o!tage difference due to the charge
. c$ The Ratio /01 is the capacitance
The unit of capacitance is called the arad !"
#ne arad is e$ual to one Coulo%b per &olt ! ' C ( &
"
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insulator
conductor
Typical capacitor geo%etries
)arallel
plates
Concentric
cylinders
Concentric
spheres
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Capacitance for Para!!e! P!ates
To ca!cu!ate capacitance, need to determinethe 2 fie!d *etween
the p!ates& 'e use -auss3
4aw, with one end of our gaussian surface
c!osed inside one p!ate, and the other c!osed
in the region *etween the p!ates
-auss:
5o or
Potentia! + force0q 6 distance:
Total charge $
on inside of plate
E*field
EAq0
=
EdV=
d
A
Ed
EAVqC 00/
===
&
&
areaA
separation
d
E= EArea= EA= q0
E = q0A
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Capacitances for simp!e geometries
7 Para!!e! P!ate Capacitor
7 Cy!indrica! "nested cy!inder$ Capacitor
7 5pherica! "nested sphere$ Capacitor
8nits of the 9arad: named after ichae! 9araday
d
AC 0
=
)/ln(2 0
ab
LC =
ab
abC
= 04
+,-+ +/0,
araday had little for%al education1 and knew little of
higher
%athe%atics such as calculus1 or even trigono%etry1 or any
but the si%plest algebra.
Discovered the electro%agnetic induction1 dia%agnetis%1
and the laws of electrolysis1 invented the use of the field
lines
His inventions for%ed the foundation of electric %otor
technology1 and it was largely due to his efforts that
electricity beca%e viable for use in technology.
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Energy 2tored in Capacitors
2nergy stored in a capacitor + !i)e a
stretched spring has potentia! energy
associated with it&
;ow much wor) is required to
charge a capacitor
