1. III. Voltage [Physics 2702]
Dr. Bill Pezzaglia
Updated 2015Feb

2. III. Voltage Electrostatic Energy Voltage2
III. Voltage
Electrostatic Energy
Voltage
Equipotentials & Electric Field

3. A. Electrostatic Energy3
A. Electrostatic Energy
REVIEW: Work Energy Theorem
REVIEW: Potential Energy
Electrostatic Potential Energy

4. 1. Work Energy Theorem (REVIEW)4
Work Definition
Conservative Forces
Work-Energy Theorem

5. a) Work (Review) Definition: Work=Force x Displacement5
Definition: Work=Force x Displacement
Units: Joule=Newton-Meter
Only force parallel to path contributes:
Hence, a force perpendicular to the path does no work!

6. b) Conservative Forces (Review)6
For a “conservative force” the work is independent of the path, it only depends upon the endpoints.
Conservative Forces are
Gravity
Electrostatics
Non-conservative Forces are:
Friction (velocity dependent)
Magnetic Forces on charges
Time dependent electric fields

7. c) Work-Energy Theorem (Review)7
Work=KE
Example: mass falling distance h in a gravity field (F=mg)

8. 2. Potential Energy (Review)8
Field Potential
Potential Energy and Work
Conservation of Energy

9. a) Field Potential (Review)9
For a conservative force, the total work done by the field on the test particle over a path can be equated to the difference of the potential energy of endpoints

10. b) Kinetic and Potential (Review)10
From the work-energy theorem: W=K
we get change in Kinetic Energy is related to change in Potential Energy
For example, if a ball drops in a gravity field a distance “h”, the potential energy decreases by U=mgh, which gives the ball kinetic energy

11. c) Conservation of Energy (Review)11
The “total energy” is the sum of potential and kinetic energy
If the Potential Theory is valid: K=-U
Then it follows that total energy is conserved

12. 3. Electrostatic Potential Energy12
Review Gravitational Potential Energy
Electrostatic Potential
Potential of assembling charges

13. a) Review: Gravitational Potential Energy13
Near surface of earth, where gravitational field is constant g=9.8 m/s2, then the change of potential energy of lifting a mass “m” up a distance “h” is just: U=mgh
For large distances, gravity follows the inverse square law. A body “m” falling from infinity to the surface of the earth (mass “M”) will have a change of potential energy of:
This would be the amount of energy that a meteor would have hitting the earth and making a big crater!

14. b) Electrostatic Potential Energy14
Electric fields also follow the inverse square law. Hence a small test charge “q” pushed from infinity onto a massive ball of charge “Q” of radius “R” will have a change of potential energy of:
Note that on previous page it was negative, while here its positive. Why?

15. c) Potential Energy of Assembling Charges15
If you assemble two charges (such as a dipole) from charges which started out at opposite ends of the universe, the energy it would take is:
The total energy “stored” by putting total charge “Q” on the ball of radius “R” is a slightly different problem, because initially there is very little field you have to fight, but as you add charge the Electric field increases and it takes that much more work to add the next piece.

16. d) Energy of a Dipole in Electric Field16
A dipole in an electric field will have a toque on it:
The work done to twist the dipole a small amount of angle would be torque times angular displacement:
The energy of a dipole in an electric field can be easily expressed as:

17. B. Voltage Definition of Voltage Sources of Voltage Measuring Voltage17
Definition of Voltage
Sources of Voltage
Measuring Voltage

18. 1a. Definition of voltage18
Potential Energy per unit test charge: (i.e. don’t want test charge to affect field)
Units: Volt=Joule/Coulomb
Voltage is the “pressure” that makes charges move (current flow).
Even if there is no test charge to experience it, voltage exists

19. 1b. Cathode Ray Tube 19
A CRT (Cathode Ray Tube) is a vaccuum tube with a large voltage across the electrodes. Electrons are emitted by the Cathode and accelerate towards the anode.
Kinetic energy the electrons gain is hence: U=eV
1 eV = 1 electron volt is the energy of one electron accelerated through one volt = 1.6x10-19 Joules. +

20. 1c. Particle Accelerators20
SLAC (Stanford Linear Accelerator Center) accelerates electrons to 50 GeV of energy
Note: the E=mc2 rest-mass energy of a proton is only 938 MeV

21. 2. Sources of Voltage Point Charge Source21
2. Sources of Voltage
Point Charge Source
Superposition of Point Charges
Batteries
Thermo and Piezoelectrics

22. 2a. Charge as Source of Voltage22
Define the voltage at infinity to be zero
Voltage a distance “r” from the center of a spherical charge Q is:

23. 2.b Voltage of a Dipole 23
Basically you use “superposition” of voltages of two monopoles.
Voltage of dipole (p=QL) along its z-axis drops off like the square of the distance!

24. 2c. Batteries are a source of voltage24
Volta ( ) “The Newton of electricity”
1800 develops first battery (approximately 30 volts)
By adding batteries together in series, one can make as big as voltage as you want.

25. 2d. Piezoelectrics etc 25 Some devices that are useful as detectors
Thermoelectrics: some materials will create a voltage across them due to a temperature difference
Pyroelectrics: heating some materials will create a voltage across them
Piezoelectrics: Pierre Curie demonstrates effect that some crystals generate a voltage when deformed

26. 26
3. Measuring Voltage
Voltmeters
Oscilloscopes
Piezoelectric

27. 3a. Voltmeters 27
A meter that measures voltage drop across a device (e.g. lamp), ideally with infinite resistance (draws no current)
Design: The classic voltmeter does not actually measure voltage directly, rather is a “galvanometer” (coil of wire around a magnetic needle) that deflects the needle in proportion to very small amount of current flowing
A BIG “shunt resistor” limits the current flow.

28. 3b. Oscilloscope 28
Oscilloscopes are used to measure voltage (especially of AC signals). They are essentially a CRT tube with deflection plates.
The amount of deflection of the beam is proportional to the voltage across the deflection plates.

29. 3c. Converse Piezoelectric Effect29
3c. Converse Piezoelectric Effect
1881 Gabriel Lippmann predicts converse should be true, changing voltage across a crystal would cause it to deform.
Used to make “piezo speaker” (e.g. in your cell phone as can be made very small and thin!)
Or, can be used as a device to measure voltage!

30. C. Equipotentials & Electric Field30
C. Equipotentials & Electric Field
Definition of Equipotentials
Electric field as gradient
diagrams

31. Notes 31 Added slide on energy of dipole in a field
Added slide on Piezoelectrics