II. Electric Field [Physics 2B] Dr. Bill Pezzaglia Updated 2017Jan25

II. Electric Field Faraday Lines of Force Electric Field 2 II. Electric Field Faraday Lines of Force Electric Field Gauss’ Law (very lightly)

Faraday’s Lines of Force Principle of “Locality” 3 A. Lines of Force Action at a Distance Faraday’s Lines of Force Principle of “Locality”

1. “Action at a Distance” 4 Newton proposes gravity must act instantaneously, regardless of distance (else angular momentum not conserved). “actio in distans” (action at a distance), no mechanism proposed to transmit gravity Sir Isaac Newton (1643-1727) "...that one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that, I believe no man, who has in philosophic matters a competent faculty of thinking, could ever fall into it." -Newton How does moon “know” the earth is there to fall towards it?

2a. Sir Humphry Davy 1778 - 1829 6 1807 Electrolysis, used to separate salts. Founds science of electrochemistry. His greatest discovery was Michael Faraday. 1813-15 takes Faraday with him on grand tour visiting Ampere and Volta.

2b. Michael Faraday 1791 - 1867 7 1821 First proposes ideas of “Lines of Force” Example: iron filings over a magnetic show field lines

2c. Electric Lines of Force 8 Electric charges create “electric field lines” Field lines start on + charges, end on – A plus charge will tend to move along these lines

2d. Other Properties 9 Field Lines can’t cross (else physics would not be deterministic, ambiguity which way to go) Density of lines is proportional to the “strength” of the force

3. Principle of Locality 10 I cannot conceive curved lines of force without the conditions of a physical existence in that intermediate space. (Michael Faraday) Argues that the field lines have independent reality Force fields exist as distortions in the “aether” of space Alternative to “action at a distance”, charges Locally interact with force lines Ideas rejected by others. He can’t put them into mathematical form.

B. Electric Field Definition of Field Sources of Field Electrodynamics 11 B. Electric Field Definition of Field Sources of Field Electrodynamics

1a. James Maxwell (1831-1879) 12 1855 essay On Faraday's Lines of Force, suggests lines are like an imaginary incompressible fluid (obeying hydrodynamic equations) 1861 paper On Physical Lines of Force, proposes “real” physical model of vortices for magnetic field

1b. Definition of Field Definition: force per unit test charge 13 1b. Definition of Field Definition: force per unit test charge (i.e. don’t want test charge to affect field) Units of Newton/Coul (or Volts/meter) So force on charge is: F=qE + E F q

14 1c. Analogy to Gravity Gravitational Force Field: force per unit test mass i.e. its an “acceleration of gravity” field Mass is the “charge” of gravity: F = mg

2. Sources of E Field Point Charge Source (monopoles Dipoles 14 2. Sources of E Field Point Charge Source (monopoles Dipoles Field of Dipole (incomplete)

15 2.a Monopole Sources A positive charge is a “source” of electric field. Field radiates outward from a point source A negative charge is a “sink” of electric field. Field radiates inward Field strength: E=kQ/r2

2.b Dipole Sources 16 An “electric dipole” is a “stick” of length “L” with + charge on one end and equal – charge on other. Dipole moment: p=QL The vector “p” points along axis from – to + charge Units (SI) is Cm Standard in Chemistry is the Debye: 1D=3.33564x10-30 Cm

2.c Field of Dipole 17 Derivation will be done on board. Basically you use “superposition” of fields of two monopoles. Field of dipole along its axis drops off like the cube of the distance!

3. Electrodynamics Force on monopole Torques on Dipoles 18 3. Electrodynamics Force on monopole Torques on Dipoles Van der Waal Forces

B.3.a: Force on a Charge (monopole) 19 Force on positive charge is in direction of field Force on negative charge is opposite direction of field + E F q - E F q

B.3.a Point Charge Electrodynamics 20 Force between monopoles is hence Coulomb’s law Force between dipole “p” and monopole “q” decreases cubically:

Torque on a dipole in an electric field is: B.3.b Torque on Dipole 21 An electric dipole will want to twist and line up with the electric field Torque on a dipole in an electric field is: Recall dipole moment p=qL

Forces between dipoles (along a line) can be shown to be: B.3.c Gradient Forces on Dipole (Van-der-Waal’s forces between molecules, e.g. Hydrogen Bonding in water) 22 If field is not constant (has a “gradient”) then there will be a force on a dipole Forces between dipoles (along a line) can be shown to be:

C. Gauss’s Law (Lightly) 23 Ignoring the mathematics, Gauss’s law (1813) has the following results:

Spherical Symmetry: 24 Electric field of a spherical ball of charge the same as a point charge: Where “r” is measured from center of ball. Note that the result is INDEPENDENT of radius of ball!

Field is zero inside a conductor 25 Consider a solid conducting sphere. Electric charge will be pushed to surface Electric field inside conductor is zero

Electric Field inside a conductor is ZERO 26 Electric Field inside a conductor is ZERO Example of Faraday Cage: An external electrical field causes the charges to rearrange which cancels the field inside.

Cylindrical Symmetry: 27 Electric field of a charge “Q” spread out on a long cylinder (length “L”) is:spherical ball of charge the same as a point charge: e.g. a line charge, or charge on a wire Note that the result is INDEPENDENT of radius of cylinder.

c. Plane Geometry 28 Consider a large flat sheet (area “A”) with charge “Q” spread out uniformly. The electric field outside is constant [Laplace 1813]. With the application of superposition principle, you can show that parallel plates of opposite charge have a constant field between (and zero outside).

References 29 http://maxwell.byu.edu/~spencerr/phys442/node4.html http://en.wikipedia.org/wiki/Timeline_of_Fundamental_Physics_Discoveries http://www.oneillselectronicmuseum.com/index.html