III. Voltage Dr. Bill Pezzaglia Updated 2012Aug06

A. Voltage 1)Electrostatic Energy 2)Electric Potential (Voltage) 3)Capacitance 2

1. Electrostatic Potential Energy a)Review Gravitational Potential Energy b)Electrostatic Potential 3

a) Review: Gravitational Potential Energy Near surface of earth, where gravitational field is constant g=9.8 m/s 2, 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! 4

b) Electrostatic Potential Energy 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: 5 Note: energy of two positive (or two negative) charges is positive Energy of positive and negative charge is negative

2. Voltage a)Definition of Voltage b)Sources of Voltage c)Measuring Voltage 6

2a. Definition of voltage 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 7

2ai. Cathode Ray Tube A CRT (Cathode Ray Tube) is a vacuum 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=e  V 1 eV = 1 electron volt is the energy of one electron accelerated through one volt = 1.6x Joules. 8

2aii. Particle Accelerators SLAC (Stanford Linear Accelerator Center) accelerates electrons to 50 GeV of energy Note: the E=mc 2 rest-mass energy of a proton is only 938 MeV 9

2b. Sources of Voltage (a)Point Charge Source (b)Superposition of Point Charges (c)Batteries (d)Thermo and Piezoelectrics 10

2bi. Charge as Source of Voltage Define the voltage at infinity to be zero Voltage a distance “r” from the center of a spherical charge Q is: 11

2bii. Batteries are a source of voltage 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. 12

2biii. Piezoelectrics etc 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 13

2c. Measuring Voltage Put a “voltmeter” in parallel with element you wish to measure potential difference 14

2cii. Oscilloscope 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 plates. 15