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1
CHAPTER 24
CAPACITANCE AND
DIELECTRICS
MAJOR TOPICS
Calculating Capacitance
Capacitors in Circuits
Energy Storage in Capacitors
Dielectrics
2
Capacitors store:
Charge
Energy
+Q + ‐ ‐Q
+ ‐
+ ‐
+ ‐
+ V _
BATTERY
+ v ‐
3
The battery supplies charge to the plates.
The charge Q is proportional to V.
Choose the proportionality constant C.
C is the CAPACITANCE of the capacitor.
4
If there is charge on a plate we
learned in Chapter 21 that
there is an electric field E.
+Q + ‐ ‐Q
+ P ‐
+ ‐
+ ‐
+ V _
BATTERY
+ v ‐
5
E at P due to + plate
E at P due to ‐ plate
Both fields point to the right
d
+Q + ‐ ‐Q
+ P ‐
+ E ‐
+ ‐
+ V _ + v ‐
6
DEFINITION
From Chapter 23
Integrate from negative to positive plate
7
8
Thus for all capacitors
And for parallel plate capacitors
Parallel plate capacitors are easy:
Area and distance between plates gives C.
If know C then:
Know Q can get V
Know V can get Q
9
Other geometries are more difficult.
Consider a cylinder inside another one.
We know
10
Need
To get need as function of between
cylinders.
Choose Gaussian cylinder of length where
r
11
Gauss’s Law
12
Then
13
14
CAPACITORS IN CIRCUITS
Series
15
16
Parallel
17
18
ENERGY IN CAPACITOR AND ELECTRIC FIELD
In Chapter 23 we defined
Thus
Now charge a capacitor
dq
19
This is the amount of work to charge the
capacitor from 0 charge to a charge of Q.
20
This is the energy stored in the capacitor.
Use definition of capacitance
Or
Then for parallel plate capacitors
21
and
Energy density
Therefore
22
DIELECTRICS
Add material between plates and C
increases.
Increases by K the dielectric constant
Parallel Plate Capacitor
Define
Then can use
23
Other quantities
Energy density
Charge on capacitor connected to V.
V
Introduce dielectric
24
V dielectric
Insert dielectric and Q increases if V
remains constant.
25
Voltage across capacitor without battery.
26
27
But
So
When C not connected to battery inserting
dielectric decreases V.
28
Electric Field in dielectric.
EXAMPLE 24.10 is an excellent review of all
of these concepts.