Part 4. Electromagnetism

1. Part 4. Electromagnetism • Applications: • Computer microchips • Cell phones • Motors & generators • Bio-EM: • Heartbeat pacing • Nerve impulses • Osmosis thru cell membranes 4 fundamental laws: Maxwell’s eqs.

2. Electromagnetism • Electric Charge, Force, & Fields • Gauss’s Law • Electric Potential • Electrostatic Energy & Capacitors • Electric Current • Electric Circuits • Magnetism: Force & Field • Electromagnetic Induction • Alternating-Current Circuits • Maxwell’s Equations & EM Waves

3. 20. Electric Charge, Force, & Field Electric Charge Coulomb’s Law The Electric Field Fields of Charge Distributions Matter in Electric Fields

4. What holds your body together? What keeps a skyscraper standing? What keeps a car on the road as it turns? What governs the electronics in computers? What provides the tension in a climbing rope? What enables the photosynthesis of plants? Ans: electric forces. All macroscopic phenomena are governed by gravity & EM forces. • Notable effective forces of electrical origin: • Tension • Normal Forces • Compression • Friction • Most forces in chemistry & biology

5. What’s the fundamental criterion for initiating a lightning strike? Ans. E > 3 MV/m

6. 20.1. Electric Charge 2 kinds of charges: + & . Total charge = algebraic sum of all charges. Like charges repel. Opposite charges attract. All electrons have charge e. All protons have charge +e. = elementary charge 1st measured by Millikan on oil drops. Theory (standard model) : basic unit of charge (carried by quark) = 1/3 e. Quark confinement  no free quark can be observed.  Smallest observable charge is e. Conservation of charge: total charge in a closed region is always the same.

7. 20.2. Coulomb’s Law “Insulators” can be charged by rubbing. Examples: Rubbed balloon sticks to clothing. 2 rubbed balloons repel each other. Socks from dryer cling to clothings. Bits of styrofoam cling to hand. Walk across carpet & feel shock touching doorknob. Ground or low energy state of matter tends to be charge neutral.

8. Triboelectric Series Steel (No charge) Wood (Small negative charge) Lucite Amber Sealing wax Acrylic Polystyrene Rubber balloon Resins Hard rubber Nickel, Copper Sulfur Brass, Silver Gold, Platinum Acetate, Rayon Synthetic rubber Polyester Styrene (Styrofoam) Orlon Plastic wrap Polyurethane Polyethylene (like Scotch tape) Polypropylene Vinyl (PVC) Silicon Teflon Silicone rubber Ebonite  Most negatively charged Most positively charged + Air Human skin Leather Rabbit's fur Glass Quartz Mica Human hair Nylon Wool Lead Cat's fur Silk Aluminium Paper (Small positive charge) Cotton (No charge) 0

9. Coulomb’s law (force between 2 point charges) : [q] = Coulomb = C

10. GOT IT? 20.1. • Charge q1 is at x = 1 m, y = 0. • What is the unit vector r in F12 if q2 is located at • the origin, • x = 0, y = 1 m ? • Explain why you can answer without knowing the sign of either charge. (a) (b)

11. Example 20.1. Force Between Two Charges A 1.0 C charge is at x = 1.0 cm, & a 1.5 C charge is at x = 3.0 cm. What force does the positive charge exert on the negative one? How would the force change if the distance between the charges tripled? Distance tripled  force drops by 1/32.

12. Conceptual Example 20.1. Gravity & Electric Force The electric force is far stronger than the gravitational force, yet gravity is much more obvious in everyday life. Why? Only 1 kind of gravitational “charge”  forces from different parts of a source tend to reinforce. 2 kinds of electric charges  forces from different parts of a neutral source tend to cancel out.

13. Making the Connection Compare the magnitudes of the electric & gravitational forces between an electron & a proton.

14. Point Charges & the Superposition Principle Extension of Coulomb’s law (point charges) to charge distributions. Superposition principle: Fnet F23 F13 Independent of each other Task: Find net force on q3 .

15. Example 20.2. Raindrops Charged raindrops are responsible for thunderstorms. Two drops with equal charge q are on the x-axis at x = a. Find the electric force on a 3rd drop with charge Q at any point on the y-axis. y F1 F2 Q r r y q q   x x1 = a x2 = a

16. 20.3. The Electric Field Electric field E at r = Electric force on unit point charge at r. F = electric force on point charge q. E = F/q [ E ] = N / C = V / m V = Volt g = F/m Implicit assumption: q doesn’t disturb E. Rigorous definition: Gravitational field Electric field

17. Force approach: Charges interact at a distance (difficult to manage when many charges are present). Fails when charge distributions are not known. Field approach: Charge interacts only with field at its position. No need to know how field is generated. Given E:

18. Example 20.3. Thunderstorm A charged raindrop carrying 10 C experiences a force of 0.30 N in the +x direction. What’s the electric field at its location? What would the force be on a 5.0 C drop at the same point?

19. The Field of a Point Charge Field at r from point charge q : Field vectors for a negative point charge.

20. 20.4. Fields of Charge Distributions (Discrete sources) Superposition principle  (Point charges)

21. Example 20.4. Two Protons Two protons are 3.6 nm apart. Find the electric field at a point between them, 1.2 nm from one of them. Find the force on an electron at this point. 3.6 nm P x 1.2 nm 2.4 nm

22. The Electric Dipole Electric dipole = Two point charges of equal magnitude but opposite charges separated by a small distance.. Examples: Polar molecules. Heart muscle during contraction  Electrocardiograph (EKG) Radio & TV antennas. H2O

23. Example 20.5. Modeling a Molecule A molecule is modeled as a positive charge q at x = a, and a negative charge q at x =  a. Evaluate the electric field on the y-axis. Find an approximate expression valid at large distances (y >> a). y E2 E Q = 1 E1 r r y q q   x x1 = a x2 = a (y >> a)

24. Dipole ( q with separation d ): for r >> d = 2a Typical of neutral, non-spherical, charge distributions ( d ~ size ). Dipole moment :p = q d. d = vector from q to +q y On perpendicular bisector: E2 E Q = 1 On dipole axis: E1 r r y q (Prob 習題 51) q   x x1 = d/2 x2 = d/2 p

25. Continuous Charge Distributions All charge distributions are ultimately discrete ( mostly protons & electrons ). Continuum approximation: Good for macroscopic bodies. Volume charge density  [ C/m3 ] Surface charge density  [ C/m2 ] Line charge density  [ C/m ]

26. Example 20.6. Charged Ring A ring of radius a carries a uniformly distributed charge Q. Find E at any point on the axis of the ring. By symmetry, E has only axial (x-) component. On axis of uniformly charged ring

27. Example 20.7. Power Line A long electric power line running along the x-axis carries a uniform charge density  [C/m]. Find E on the y-axis, assuming the wire to be infinitely long. y dEy By symmetry, E has only y- component. dE dE P r r y x dq x dq Perpendicular to an infinite wire

28. 20.5. Matter in Electric Fields Point Charges in Electric Fields Newton’s 2nd law  (point charge in field E)  Trajectory determined by charge-to-mass ratio q/m. Constant E  constant a. E.g., CRT, inkjet printer, …. Uniform field between charged plates (capacitors).

29. Example 20.8. Electrostatic Analyzer Two curved metal plates establish a field of strength E = E0( b/r ), where E0 & b are constants. E points toward the center of curvature, & r is the distance to the center. Find speed v with which a proton entering vertically from below will leave the device moving horizontally. Too fast, hits outer wall For a uniform circular motion:  Too slow, hits inner wall

30. GOT IT? 20.3. • An electron, a proton, a deuteron (1p, 1n), a 3He nucleus (2p, 1n), a 4He nucleus (2p, 2n), a 13C nucleus (6p, 7n), & an 16O nucleus (8 p, 8 n) all find themselves in the same electric field. • Rank order their accelerations from lowest to highest assuming • p & n have the same mass. • The mass of a composite particle is the sum of the masses of its constituents. 1800 1/1 1/2 2/3 2/4 6/13 8/16 Ans: 13C, (16O, 4He, deuteron), 3He, p, e.

31. Dipoles in Electric Fields Uniform E: Total force: Torque about center of dipole: = dipole moment Work done by E to rotate dipole : t // tangent Potential energy of dipole in E (i= /2) ( U = 0 for p  E )

32. Non-uniform field: Total force: Example: dipole-dipole interaction | F | > | F+ | c.f. Van der Waals interaction, long range part. Force on  end of B is stronger; hence net force is toward A

33. Application: Microwave Cooking & Liquid Crystals Microwave oven: GHz EM field vibrates (dipolar) H2O molecules in food  heats up. Liquid Crystal Display (LCD) dipolar molecules aligned but positions irregular

34. Exploded view of a TN (Twisted Nematic) liquid crystal cell showing the states in an OFF state (left), and an ON state with voltage applied (right)

35. Conductors, Insulators, & Dielectrics Bulk matter consists of point charges: e & p. Conductors: charges free to move (  electric currents ), e.g., e (metal), ion ( electrolytes ), e+ion (plasma). Insulators: charges are bounded. Dielectrics: insulators with intrinsic / induced dipoles. internal field from dipoles Induced dipole Alignment of intrinsic dipoles.