Physics 202, Lecture 4
Today’s Topics
„
„
Conductors in Electrostatic Equilibrium (Ch. 24.4)
Electric Potential (Ch. 25-Part I)
„ Electric Potential Energy & Electric Potential
„ Electric Potential And Electric Field
Conductors And Electrostatic Equilibrium
‰ Conductors: Total charge are initially balanced (=0) but negative
charge (electrons) are able to move freely inside its body.
Î capable of redistributing charges when subject to an external
electric field.
‰ Charge redistribution Æ eventually electrostatic equilibrium.
E
E
™ Expected from preview:
Conductors
Conservative force, electric energy, electric potential
difference, voltage….
- - - - - - -
- - - - -
E=0
+ + + + + + +
E
Æ
Initial
Properties of Electrostatic Equilibrium
‰ Once in electrostatic equilibrium
ƒ The electric field is always zero inside the conductor
ƒ E field on the surface of conductor is always normal to the
surface,
ƒ and has a magnitude of σ/ε0 (Show using Gauss’s law )
ƒ All net charges reside on the surface of conductor (i.e. no net
charge inside the body of a conductor).
transient, <10-16s
Æ equilibrium
(right after E applied)
Potential Energy (Phy201 Review)
‰ Ch-8: path independent work Æ conservative force.
‰ e.g. Gravitational Force is a conservative force (Ch-13):
r
mm
F12 = −G 1 2 2 r̂12
r
W = ∫ F • ds =
path
Gm1m2 Gm1m2
−
rf
ri
ÎG it ti
ÎGravitational
l Potential
P t ti l energy:
ƒ The electric field is also zero inside any cavity within the
conductor. (why?)
ƒ Electric potential is the same over the whole conductor (Ch. 25)
U =−
path independent!
Gm1m2
r
¾ Electric Force:
The above properties are valid regardless of the shape
and the total charge of the conductors !
r
qq
F12 = ke 1 2 2 r̂12
r
Electric
Potential Energy
U=
ke q1q2
r
1
Electric Potential Energy
Example: Three Charge system
‰ Electric energy between two point charges:
U = U-U∞ = Ke q0q/r
ƒ U is a scalar quantity
ƒ U=0 @ r= ∞ (convenient convention)
ƒ U can be positive or negative
• +: between like-sign charges
• -: between opposite charges
ƒ SI unit: Joule (J)
q
‰ What is the work required to assemble the three
charge system as shown? (q1=q2=q3=Q)
Answer: ke 3Q2/a (see board)
q3
r
a
a
q0
‰ Electric potential energy for system of multiple
charges/charge distributions:
U=Σ of all combination of pairs.
‰ Quiz: What if q1=q2=Q but q3=-Q ?
Answer: -keQ2/a
q1
a
q2
Integral if continuous distribution
Electric Potential Energy:
Charge In An Electric Field
‰ Charge q is subject an electric force in electric field E
Electric Potential Difference
‰ Electric Potential Energy: q In a Generic E. Field
B
ΔU = U B − U A = − q ∫ E • ds = qΔV
F=qE
A
‰ Work done by electric force:
system energy
f
f
W = ∫ F • ds = q ∫ E • ds = − ΔU
i
ΔU = U f − U i = − q ∫ E • ds
source
‰ Electric Potential Difference
i
f
test
ΔV ≡
B
ΔU
= − ∫ E • ds = VB − VA
A
q
i
independent of q
2
Properties of Electric Potential Difference
‰ It is defined upon the fact that the electric force is a
conservative force.
‰ It is associated to the source field only and is
independent of test charge.
‰ It has a unit: J/C ≡ Volt (V)
‰ It is commonly called as just Potential,
Potential but it is
meaningful only as potential difference VB-VA.
‰ Usually a convenient point (remote, earth..) is chosen
as “ground” Æ ΔV=V-(VA≡0) =V
‰ It is a scalar quantity. (No vector operation necessary!)
‰ ΔU=qΔV
Exercise 2: E. Potential and Point Charges
‰ In the configuration shown,
ƒ Find the potential difference VB-VA
B
Exercise 1: Potential In Uniform E. Field
‰ In the uniform electric field shown.
Find E. potential at points: B,C,D,G
If a charge +q is placed at B,
ƒ
what is the potential energy UB? (UA≡0)
A
VA=0
If a charge –q is at B, what is UB?
‰
C
D
ƒ
ƒ
B
G
d
ƒ
If a negative charge -q is initially at rest at G,
will it move to A or B?
ƒ
What is the kinetic energy when it reaches A?
Exercise 3: Cathode Ray Tube (CRT)
‰ Electrons are emitted with almost zero velocity on plate C,
what is the energy per electron when they reach plate A?
(Do with your TA)
Answer:
rB
VB-VA = ke(q/rB-q/rA)
A
rA
q
(Exercise with your TA)
VA-VC
=12000V
3
Visualization of Electric Potential
Equipotential Lines
Reminder: A Picture to Remember
+q
-q
higher potential V
E
F=qE
ΔU=qΔV
W =ΔU
ΔV=-∫Eds
lower V
¾ Field lines always point towards lower electric potential
¾ Field lines and equal-potential lines are always at a normal angle.
¾ In an electric field:
ƒ a +q is always subject a force in the same direction of field line.
(i.e. towards lower V)
ƒ a -q is always subject a force in the opposite direction of field
line. (i.e. towards higher V)
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