Chapter 23: Electrostatic Energy & Capacitance Chapter 24: Electric Current & Ohm’s law
Tuesday September 27th
• Review of Mini Exam 2 • Review of Capacitance and Electrostatic Energy • Capacitors in series and parallel
• Demonstration and example • Dielectrics and capacitance
• Demonstration and explanation • Conductors under dynamic conditions
• Current, current density, drift velovity • Ohm’s law
Reading: up to page 410 in the text book (Ch. 24)
Capacitors • The transfer of charge from one terminal of the capacitor to the other creates the electric field.
• Where there is an electric field, there must be a potential difference, leading to the following definition of capacitance C:
C = Q
!V or Q = C!V
• Q represents the magnitude of the excess charge on either plate. Another way of thinking of it is the charge that was transferred between the plates.
SI unit of capacitance: 1 farad (F) = 1 coulomb/volt
(after Michael Faraday)
V (q)
q U
Energy stored in a Capacitor
U = q2
2C=
CV( )2
2C= 1
2 CV 2
= q2
2C= 1
2qC
q = 12 qV
Just like energy stored in a spring
Capacitors connected in series
1 2
1 1 1
eqC C C= +
1 1neq nC C
=∑In fact:
Capacitors connected in parallel
1 1q C V= Δ
2 2q C V= Δ1 2 eqq q C V+ = Δ
( )1 2 eqC C V C V+ Δ = Δ
1 2eqC C C= +
+q2 -q2
-q1 +q1
!V+(q1+q2) -(q1+q2)
!V
More Challenging Example
C1 C2
C3
C4 C5
A
B
What is capacitance between points A and B
A dielectric in an electric field
Electric dipoles in an electric field Non-polar atoms in an electric field
A dielectric in an electric field
!E =!E0 +
!E'
E = E0 - E' E' opposes E0 Linear materials: E' ! E, or E' = "eE
! E = E0 " #eE, or E0 = 1+ #e( )E
!e is the electric susceptibility (dimensionless)
A dielectric in an electric field
0 01 1 ( 1 )
1 e ee e
E E E κ χχ κ
⇒ = = = ++
Linear materials: E0 = 1+ !e( )E
!e is the electric susceptibility (dimensionless)" e is the dielectric constant (dimensionless)# =" e#o is the permittivity
A dielectric in an electric field
Linear materials: E0 = 1+ !e( )E
If E =
E0
! e
, then "V ="V0
! e
= 1! e
QdA#o
Isolated capacitor: Potential difference without dielectric
Actual potential difference with dielectric Potential decreases due to screening of field by surface charge
Capacitor with dielectric between plates
Linear materials: E0 = 1+ !e( )E
!V =
!V0
" e
= 1" e
QdA#o
Isolated capacitor:
! Ceff =
Q"V
=# e
$o Ad
=# eC
Capacitance increases:
Conductors in E-fields: dynamic conditions • If the E-field is maintained,
then the dynamics persist, i.e., charge continues to flow indefinitely.
• This is no longer strictly the domain of electrostatics. • Note the direction of flow of
the charge carriers (electrons).
Electrical current: I = dQ
dt! "Q
"tSI unit: 1 ampere (A) = 1 coulomb per second (C/s)
+ E
E
E
E E
I