Download Physics 18

Physics
Chapter 18:
Electrical Energy
and Capacitance
Electrical Energy and
Capacitance
• Electric Field
– Surrounds All Charged Particles
• Electric Force
– Applied by an Electric Field
kq1q2
2
F
kq
r
E

 2
qo
qo
r
F
E
qo
q1q2
F k 2
r
Electrical Energy and
Capacitance
• Electrical Potential Energy (PE)
– Electrical Force Can Move Charged Particles
– Movement of a Mass Over a Distance is Work
– Electrical Force Does Work in the Form of
Electrical Potential Energy
ME  KE  PEg  PEelastic  PEelectric
Electrical Energy and
Capacitance
• Electrical Potential Energy (PE)
– Uniform Electric Field
– How about something other than particles?
Electrical Energy and
Capacitance
• Electrical Potential Energy (PE)
– Uniform Electric Field
++++++++++++++++
Charged Plates
- - - - - - - - - - - - - - - -
Electrical Energy and
Capacitance
• Electrical Potential Energy (PE)
– Uniform Electric Field
++++++++++++++++
Direction of E Field
- - - - - - - - - - - - - - - -
Charged Plates
Electrical Energy and
Capacitance
• Electrical Potential Energy (PE)
– Uniform Electric Field
++++++++++++++++
+q0i
E Field
- - - - - - - - - - - - - - - -
Charged Plates
Electrical Energy and
Capacitance
• Electrical Potential Energy (PE)
– Uniform Electric Field
++++++++++++++++
+q0i
Displacement
Due to Applied
Force
E Field
+q0f
- - - - - - - - - - - - - - - -
Charged Plates
Electrical Energy and
Capacitance
• Electrical Potential Energy (PE)
– In the Same Way that Work is done by
Gravitational Force…Wg=DPEg
– Electric Force does Work as a Force Vector on
a Test Charge (q0)
DW  DPE
E field
Felectric

q0
Electrical Energy and
Capacitance
• Electrical Potential Energy (PE)
DW DPE

q0
q0
E field
Felectric

q0
DPEelectric  qEd
PE Decreases for a + Charge
PE Increases for a - Charge
Electrical Energy and
Capacitance
• Electrical Potential Energy (PE)
– Also Applies to Displacement of
Charged particles Due to Other
Charged Particles
q1q2
DPEelectric  k
d
DPEelectric  qEd
Electrical Energy and
Capacitance
• Electrical Potential Energy (PE)
– Units
• Energy, so…
– Joules
q1q2
DPEelectric  k
d
DPEelectric  qEd
Electrical Energy and
Capacitance
• Electric Potential Difference (V)
– As the Positive Charge Moves from the
Positive Plate to the Negative Plate the PE
Decreases
– At Any Point in the
Field, the PE will
Increase with
Increased Charge
++++++++++++++++
+q0i
+q0f
- - - - - - - - - - - - - - - -
Electrical Energy and
Capacitance
• Electric Potential Difference (V)
– This Potential Difference is Measured in
Joules/Coulomb (Energy/Charge)
– The Units of Potential Difference are Volts (V)
++++++++++++++++
DPE
V
q0
+q0i
+q0f
- - - - - - - - - - - - - - - -
Electrical Energy and
Capacitance
• Electric Potential Difference (V)
DPE
V
q0
DPEelectric  qEd
++++++++++++++++
V  Ed
+q0i
+q0f
- - - - - - - - - - - - - - - -
Electrical Energy and
Capacitance
• Electric Potential Difference (V)
DPE
V
q0
q1q2
DPEelectric  k
d
q
V k
r
++++++++++++++++
+q0i
+q0f
- - - - - - - - - - - - - - - -
Electrical Energy and
Capacitance
• Electric Potential Difference
– Problem “PE Difference”
• q0 = 3x10-9C
• Wa-b = 6x10-8J
– What is DEPE?
– What is DV?
++++++++++++++++
DEPE  Wab
DV 

q0
q0
q0a
E
q0b
----------------
Electrical Energy and
Capacitance
• Electric Potential Difference
– Solution “PE Difference”
• q0 = 3x10-9C
• Wa-b = 6x10-8J
– What is DEPE?
DEPE = -Wa-b = -6x10-8J
++++++++++++++++
DEPE  Wab
DV 

q0
q0
q0a
E
q0b
----------------
Electrical Energy and
Capacitance
• Electric Potential Difference
– Solution “PE Difference”
• q0 = 3x10-9C
• Wa-b = 6x10-8J
– What is DV?
8
DEPE  6 x10 J
DV 

 20V
9
q0
3x10 C
++++++++++++++++
q0a
E
q0b
----------------
Electrical Energy and
Capacitance
• Electric Potential Difference
– Note in the Previous Problem
• q0 had a Positive Charge
• A Positive Charge Moves from Higher PE to Lower PE
• A Negative Charge Moves from Lower PE to Higher PE
++++++++++++++++
q0a
E
q0b
----------------
++++++++++++++++
-q0b
E
-q0a
----------------
Electrical Energy and
Capacitance
• Electric Potential Difference
– Problem “The Light Will Come
On”
•
•
•
•
Electron Particle: q1 = 1.6x10-19C
System Voltage: V = 12 J/C
System Power (Light) = 40 W
Time = 1 minute
– How Many Electrons Will Pass,
and in Which Direction?
++++++++++++++++
-q0
E
-q0
----------------
Electrical Energy and
Capacitance
• Electric Potential Difference
– Solution “The Light Will Burn”
•
•
•
•
Electron Particle: q1 = 1.6x10-19C
System Voltage: V = 12 J/C
System Power (Light) = 40 W
Time = 1 minute
– Energy = Power x Time
DEPE = 40W x 60s = 2400 w/s (J)
q0 = DEPE/DV = 2400J/12V =
2x102C
++++++++++++++++
-q0
E
-q0
----------------
Electrical Energy and
Capacitance
• Electric Potential Difference
– Solution “The Light Will Burn”
q0 = DEPE/DV = 2400J/12V = 2x102C
– Total Particles:
• q0 / q (-e) = (2x102C) / (1.6x10-19C)
• = 1.3x1021
– Direction?
• “A Negative Charge Moves from
Lower PE to Higher PE”
++++++++++++++++
-q0b
E
-q0a
----------------
Electrical Energy and
Capacitance
• Electric Potential Difference
– Energy, The Big Picture
•
•
•
•
•
Translational KE
Rotational KE
Gravitational PE
Elastic PE
Electric PE
1 2 1 2
1 2
E  mv  I  mgh  kx  EPE
2
2
2
Electrical Energy and
Capacitance
• Electric Potential Difference
– Problem: “Energy Conserved?”
• Particle Moves from Point “a” to Point “b” by Electric Force
– Mass = 3.6x10-3kg
– Charge (q0) = 6x10-3C
• DV = 25V
• V0 = 0
– What is the Particle Speed at Point “b”?
+
+
+
+
+
+
a
b
-
Electrical Energy and
Capacitance
• Electric Potential Difference
– Solution: “Energy Conserved?”
– Mass = 3.6x10-3kg
– Charge (q0) = 6x10-3C
• DV = 25V
• V0 = 0
– Rotation = 0
– Elasticity = 0
– Enet = Translational KE + Gravitational PE + EPE
Electrical Energy and
Capacitance
• Electric Potential Difference
– Solution: “Energy Conserved?”
– Mass = 3.6x10-3kg
– Charge (q0) = 6x10-3C
• DV = 25V
• V0 = 0
– ha = hb (Horizontal Movement Only)
– EPEa – EPEb = q0(va-vb)
– So…
1
1
2
2
mvb  mva  q0 (va  vb )
2
2
Electrical Energy and
Capacitance
• Electric Potential
Difference
1
1
2
2
mvb  mva  q0 (Va  Vb )
2
2
– Solution: “Energy
Conserved?”
– Mass = 3.6x10-3kg
– Charge (q0) = 6x10-3C
• DV = 25V
• V0 = 0
2q0 (Va  Vb )
vb 
m
Electrical Energy and
Capacitance
• Electric Potential
Difference
– Solution: “Energy
Conserved?”
– Mass = 3.6x10-3kg
– Charge (q0) = 6x10-3C
2q0 (va  vb )
vb 
m
• DV = 25V
• V0 = 0
2(6 x103 C )( 25V )
vb 
 9.1m / s
3
3.6 x10 kg
Electrical Energy and
Capacitance
• Homework
–Pages 683-685
• Problems:
–12 (2.6x104V)
–13 (-154V)
–32 (4000V/m)
Electrical Energy and
Capacitance
• Capacitors
– Two Conductors Placed Near Each
Other but Not Touching
– The Area Between the Conductors
is Filled With an Insulating
Material (Dielectric)
Electrical Energy and
Capacitance
• Capacitors
– Dielectric
• Contains Dipolar Molecules
+ Charge on One End
- Charge on the Other End
E
+
+
+
+
+
+
+
Dielectric
Material
-
Electrical Energy and
Capacitance
• Capacitors
– Dielectric
• Each Molecule Accepts
Charge (q)
E
+ +
+
+
+
+
+
+
Dielectric
Material
-
+
-
Electrical Energy and
Capacitance
• Capacitors
– Dielectric
• Each Molecule Accepts
Charge (q)
• Entire Dielectric
Material Becomes
Charged
E
+
+
+
+
+
+
+
-
+
+
+
Dielectric
+
Material
+
+
+
-
Electrical Energy and
Capacitance
• Capacitors
– Store Electric Charge
– Positive and Negative Terminals
Carry the Same Charge Magnitude
Electrical Energy and
Capacitance
• Capacitors
– Capacitance (C)
• The Ability of the Capacitor to Store Charge
E
q
C
DV
+
+
+
+
+
+
+
Dielectric
Material
-
Electrical Energy and
Capacitance
• Capacitors
– Units
• coulomb/volt
• Farad
– (after Michael Faraday)
q
C
DV
E
+
+
+
+
+
+
+
Dielectric
Material
-
Electrical Energy and
Capacitance
• Capacitance
– Varies with Type, Size, and Shape
• Parallel Plate
– Permittivity of Free Space
– 8.85x10-12C2/Nm2
A
C  0
d
E
+
+
+
+
+
+
+
Dielectric
Material
-
Electrical Energy and
Capacitance
• Capacitors
– Due to the Charged
Molecules of the
Dielectric, the Electric
Field (E) is Reduced
E
+
+
+
+
+
+
+
-
+
+
+
Dielectric
+
Material
+
+
+
-
Electrical Energy and
Capacitance
• Capacitors and Electric PE
– Stored Charge is Stored Electric Potential
Energy
1
PE  qDV
2
E
+
+
+
+
+
+
+
-
+
+
+
Dielectric
+
Material
+
+
+
-
Electrical Energy and
Capacitance
• Capacitors and Electric PE
– Stored Charge is Stored Electric Potential
Energy
q
1
C
PE  qDV
D
V
2
1
2
PE  C (DV )
2
2
q
PE 
2C
Electrical Energy and
Capacitance
• Homework
–Pages 684-686
• Problems:
–26 (7.2x10-11C)
–27 (a, 1.3x10-3C b, 4.2J)
–43 (4x10-6F)