Review and Overview
ÎCoulomb’s
law and Gauss’ law
(equivalent)
Coulomb’s
law
Gauss’
law
E field ---- F=qE ---- Force F
(integrate)
(integrate)
(differentiate)
(differentiate)
Potential V --- U=qV ---Energy U
ÎApplications:
Capacitance (Ch. 25)
Electric circuits (Ch. 26)
PHY2049: Chapter 25
Current I=dq/dt
1
Ch. 25 Subjects
ÎCapacitor
and units
and Capacitance: definitions
ÎCapacitance:
ÎCapacitors
ÎEnergy
calculation
in parallel and series
stored in electric field
ÎDielectrics
(insulators)
PHY2049: Chapter 25
2
Capacitors
Capacitors
Capacitors on a
computer
motherboard
PHY2049: Chapter 25
3
Definitions and Units
Î
Capacitor
Two conductors, electrically isolated from each other
‹ Particularly when the pair is used as a device in an electronic
circuit to store charge and for other purposes
‹
Î
Capacitance
q = CV
C is a constant that characterizes given pair of conductors in given
configuration (Can be generalize to a single conductor. Read
Section 25-3.)
‹ For given (applied) V, capacitor with larger C stores more q
‹ For given q, smaller V appears in capacitor with larger C
‹
Î
Units
F (farad)
‹
1 F = 1 C/V (C: coulomb, not capacitance)
Note: ε0=8.854x10-12 C2/N m2=(same value) F/m
PHY2049: Chapter 25
4
Why do we consider only +q and –q
forming a pair? Why not +q and –Q?
Let us postpone the question for the
moment.
PHY2049: Chapter 25
5
Capacitance calculation 1: parallel plates
q
∫SE ⋅ dA = EA + 0 = ε 0
1 q
E=
ε0 A
Gauss’ law
Solve for E
1 qd
V = − ∫ E ⋅ ds = Ed =
−
ε0 A
+
Potential difference (Do not worry about sign.
+ is always high.)
C=
q
A
= ε0
V
d
Capacitance
[capacitance]=ε0 x [length]
F = F/m x m
PHY2049: Chapter 25
6
Capacitance calculation 2: coaxial cylinders
Ignore ends, approximating
cylinder to be infinitely long
∫ E ⋅ dA = E (2πrL) + 0 =
S
E=
q
ε0
1 q
2πε 0 rL
1 q b dr
V = − ∫ E ⋅ ds =
−
2πε 0 L ∫a r
Gauss’ law
Solve for E
+
b
lnb − lna = ln 
a
Potential difference (Do not worry about sign.
+ is always high.)
Radii a and b.
[length]
◊
[capacitance]=ε
q
L
0
C = = 2πε 0
V
ln (b a ) ◊ Depends only weakly on radii
◊ Inner conductor cannot be approximated to
Capacitance
be line with no thickness. Then C=∞.
PHY2049: Chapter 25
7