II. Electric Field [Physics 2702]

1. II. Electric Field[Physics 2702] Dr. Bill Pezzaglia Updated 2015Feb09

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

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

4. 4 1. “Action at a Distance” • 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 falltowards it?

5. 6 2a. Sir Humphry Davy1778 - 1829 • 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.

6. 7 2b. Michael Faraday1791 - 1867 • 1821 First proposes ideas of “Lines of Force” • Example: iron filings over a magnetic show field lines

7. 8 2c. Electric Lines of Force • Electric charges create “electric field lines” • Field lines start on + charges, end on – • A plus charge will tend to move along these lines

8. 9 2d. Other Properties • 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

9. 10 3. Principle of Locality 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.

10. 11 B. Electric Field • Definition of Field • Sources of Field • Electrodynamics

11. 12 1a. James Maxwell (1831-1879) • 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

12. 13 q + F E 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

13. 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

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

15. 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

16. 16 2.b Dipole Sources • 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

17. 17 2.c Field of Dipole • 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!

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

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

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

21. 21 B.3.b Torque on Dipole • 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 momentp=qL

22. 22 B.3.c Gradient Forces on Dipole(Van-der-Waal’s forces between molecules, e.g. Hydrogen Bonding in water) • 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:

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

24. 24 Spherical Symmetry: 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!

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

26. 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.

27. Cylindrical Symmetry: 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: 27 e.g. a line charge, or charge on a wire Note that the result is INDEPENDENT of radius of cylinder.

28. 28 c. Plane Geometry 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).

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