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

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

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

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

a) Work (Review) Definition: Work=Force x Displacement 5 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!

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

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

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

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

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

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

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

a) Review: Gravitational Potential Energy 13 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!

b) Electrostatic Potential Energy 14 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?

c) Potential Energy of Assembling Charges 15 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.

d) Energy of a Dipole in Electric Field 16 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:

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

1a. Definition of voltage 18 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

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. + http://www.youtube.com/v/XU8nMKkzbT8?f=videos&app=youtube_gdata&autoplay=1 https://www.youtube.com/watch?v=CsjLYLW_3G0

1c. Particle Accelerators 20 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

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

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

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!

2c. Batteries are a source of voltage 24 Volta (1745-1827) “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. http://www.corrosion-doctors.org/Biographies/VoltaBio.htm

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: 1880 Pierre Curie demonstrates effect that some crystals generate a voltage when deformed

26 3. Measuring Voltage Voltmeters Oscilloscopes Piezoelectric

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.

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.

3c. Converse Piezoelectric Effect 29 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!

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

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