Neil deGrasse Tyson on Astronomy and the Universe

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Physics Distinguished Lecture Series

• Neil deGrasse Tyson on Astronomy and the Universe
• Astrophysicist
• Director Hayden Planetarium
• Host of Nova Science Now
• Lecture Feb 2nd, 730, Union Theater
• Free tickets at physics department office or
  Union Box Office
• Note Moving office hours to 11-12 starting next
  week.

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Electrical Energy Capacitors

• Capacitors and Dielectrics
• Parallel Plate Capacitor
• Energy Stored in Capacitors

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From Before

• How to calculate the electric force and field
  from charges.

• Work done by an electric force(conservative
  force) and potential energy. Electric potential
  energy can be converted into kinetic energy when
  a charge is released.

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Work and D Potential Energy
W F d cos(q) Gravity Electric

• Brick raised yi? yf

• Charge moved ? ? rf
• FE kq1q2/r2 (left)
• E kQ/r2
• WE -kq1q2/rf
• DPEE kq1q2/rf
• V k Q/r

• FG mg (down)
• WG -mgh
• DPEG mgh

yf?
h
yi?
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Electric Potential
Potential Energy per (test) charge q For
isolated charge Q
Think of the potential due to Q as giving rise
to a potential energy when combined with a test
charge q Just as the electric field of Q gives
rise to a force on test charge q Electric field
points in the direction down the slope of the
potential hill
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Conductors

• Charges can move freely inside a conductor
• Electric field vanishes inside the conductor
• The electric field is perpendicular to the
  surface of the conductor
• The electric potential is constant inside the
  conductor

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Electric Field outside Charged Conducting Plate

• Electric field perpendicular to the conductors
  surface
• Charge distributes uniformly
• Can find E from Gauss Law
• Gauss Law
• Electric field flips direction if charge on the
  plate is negative

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Parallel Charged Plates

• Electric field between plates (distance d)
• Electric Potential
• Capacitor a device for storing charge

(Vacuum Permittivity)
(capacitance)
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Electric Field in a Parallel-Plate Capacitor
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Unit for Capacitance

• CQ/V(Coulomb)/(Joule/Coulomb)
• Coulomb/Volts
• Coulomb2/JouleFarad (F)

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Volta
Coulomb
Joule
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Capacitors store Energy

• To charge a capacitor with charge Q
• ?V 0
• Move -?Q from left to right (NQ/?Qlarge)
• ????????PE0.
• ?V ?Q/C
• Move another -?Q
• ????????PE ?V ?Q?Q2/C
• ?V 2C ?Q
• Move another -?Q
• ????????PE ?V ?Q2 ?Q2/C
• ?V 3C ?Q
• Move another -?Q
• ????????PE ?V ?Q3 ?Q2/C

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Summary of facts

• Capacitors Q CV
• Energy stored in a charged capacitor
• Capacitance of a parallel plate capacitor

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Capacitance Example

• How much charge is on a 1 F capacitor which has a
  potential difference of 110 Volts?

Q CV
(1)(110) 110 Coulombs
How much energy is stored in this capacitor?
Ecap QV/2
(110) (110) / 2 6,050 Joules!
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Parallel Plate CapacitorExample

• Calculate the capacitance of a parallel plate
  capacitor made from two large square metal sheets
  1.3 m on a side, separated by 0.1 m.

A
A
d
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Capacitor Limits

• Too much charge causes discharge

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Question?

• Consider a capacitor made of two parallel
  metallic plates separated by a distance d. A new
  metal plate with thickness t is inserted between
  them without changing the charge on the original
  plates. The capacitance of the plate

1) increases 2) decreases 3) stays the same
Effective d decreasesCeA/d increases
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Dielectric

• Placing a dielectric between the plates increases
  the capacitance.
• C k C0

Dielectric constant (k gt 1)
Capacitance with dielectric
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Dielectric Constant, Strength

• Large capacitance (energy storage)
• Small gap (d)
• Breakdown voltage is material dependent
• Large area (A)
• Would like to keep the device size tolerable
• Large dielectric constant (ke0)
• Large dielectric strength
• Dielectric constant/strength of material

( permittivity of a dielectric)
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Question?

• Consider a capacitor made of two parallel
  metallic plates separated by a distance d. A
  dielectric slab with thickness t is inserted
  between them without changing the charge on the
  original plates. The energy stored in the
  capacitor

1) increases 2) decreases 3) stays the same
Effective e increasesCeA/d increasesEcapQ2/2
C decreases
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Extra
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Question
A parallel plate capacitor given a charge q. The
plates are then pulled a small distance further
apart. What happens to the charge q on each plate
of the capacitor?
1) Increases 2) Constant 3) Decreases
Remember charge is real/physical. There is no
place for the charges to go.
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Preflight
A parallel plate capacitor given a charge q. The
plates are then pulled a small distance further
apart. Which of the following apply to the
situation after the plates have been moved?
1)The capacitance increases 2)The electric field
increases 3)The voltage between the plates
increases 4)The energy stored in the capacitor
increases
C e0A/d ? C decreases!
E Q/(e0A) ? E constant
V Ed ? V increases
Ecap QV / 2 Q constant, V increased? Ecap
increases
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Preflight
Two identical parallel plate capacitors are shown
in end-view in A) of the figure. Each has a
capacitance of C.
C is directly proportional to A, so if A is
doubled, C is also doubled.
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Capacitors in Parallel

• Both ends connected together by wire

Veq

• Same voltage V1 V2

• Add Areas Ceq C1C2
• Share Charge Qeq Q1Q2

15 V
15 V
15 V
C1
C2
10 V
10 V
10 V
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Parallel Example

• A 4 mF capacitor and 6 mF capacitor are connected
  in parallel and charged to 5 volts. Calculate
  Ceq, and the charge on each capacitor.

4 mF6 mF 10 mF
Ceq C4C6
Q4 C4 V4
(4 mF)(5 V) 20 mC
Q6 C6 V6
(6 mF)(5 V) 30 mC
Qeq Ceq Veq
(10 mF)(5 V) 50 mC
Q4Q6
5 V
5 V
5 V
C4
C6
Ceq
0 V
0 V
0 V
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Capacitors in Series

• Same Charge Q1 Q2 Qeq
• Share VoltageV1V2Veq
• Add d

Q


C1


-




C2
-Q
-

-



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Series Example

• A 4 mF capacitor and 6 mF capacitor are connected
  in series and charged to 5 volts. Calculate Ceq,
  and the charge on the 4 mF capacitor.

Q CV
5 V

C4
Ceq
-

C6
-
0 V
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Capacitor Network Summary

• Parallel
• Series

Ceq C1C2
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Question?

• A solid spherical conductor is given a net
  non-zero charge. The electric potential of the
  conductor is
• largest at the center.
• largest at the surface.
• largest somewhere between center and surface.
• Constant throughout the volume.

Electric field inside a conductor is zero.
Electric field is the slope of the electric
potential - therefore, it must be constant in a
conductor.
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Question?

• Consider two isolated spherical conductors each
  having net charge Q. The spheres have radii a and
  b, where b gt a. Which sphere has the higher
  electric potential?
• The sphere of radius a.
• The sphere of radius b.
• They both have the same potential.

The charge is spread more in the larger sphere
than in the smaller sphere, but is constant
within its volume V?1/r, therefore, smaller
sphere has higher potential.
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