Electromagnetism 20. Electric Charge, Force, & Fields 21. Gauss’s Law 22. Electric Potential 23. Electrostatic Energy & Capacitors 24. Electric Current 25. Electric Circuits 26. Magnetism: Force & Field 27. Electromagnetic Induction 28. Alternating-Current Circuits 29. Maxwell’s Equations & EM Waves
20. Electric Charge, Force, & Field 1.Electric Charge 2.Coulomb’s Law 3.The Electric Field 4.Fields of Charge Distributions 5.Matter in Electric Fields
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. Notable effective forces of electrical origin: Tension Normal Forces Compression Friction Most forces in chemistry & biology All macroscopic phenomena are governed by gravity & EM forces.
What’s the fundamental criterion for initiating a lightning strike? Ans. E > 3 MV/m
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 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. 1 st measured by Millikan on oil drops. Conservation of charge: total charge in a closed region is always the same.
20.2. Coulomb’s Law 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. “Insulators” can be charged by rubbing. Ground or low energy state of matter tends to be charge neutral.
Triboelectric Series 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 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
Coulomb’s law (force between 2 point charges) : [q] = Coulomb = C
GOT IT? Charge q 1 is at x = 1 m, y = 0. What is the unit vector r in F 12 if q 2 is located at (a) the origin, (b) x = 0, y = 1 m ? Explain why you can answer without knowing the sign of either charge. (a) (b)
Example 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 1/3 2.
Conceptual Example 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.
Making the Connection Compare the magnitudes of the electric & gravitational forces between an electron & a proton.
Point Charges & the Superposition Principle Extension of Coulomb’s law (point charges) to charge distributions. Superposition principle: Independent of each other Task: Find net force on q 3. F 13 F 23 F net
Example 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 3 rd drop with charge Q at any point on the y-axis. y x x 1 = a x 2 = a q q Q y rr F1F1 F2F2
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. Gravitational fieldElectric field Implicit assumption: q doesn’t disturb E. Rigorous definition: [ E ] = N / C = V / m V = Volt g = F/m E = F/q
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:
Example 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?
The Field of a Point Charge Field vectors for a negative point charge. Field at r from point charge q :
Example 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. x 3.6 nm 1.2 nm2.4 nm P
The Electric Dipole H2OH2O 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.
Example 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 >> a) y x x 1 = a x 2 = a qq q Q = 1 y rr E1E1 E2E2 E
Dipole ( q with separation d ): for r >> d = 2a Typical of neutral, non-spherical, charge distributions ( d ~ size ). Dipole moment : p = q d. On perpendicular bisector: On dipole axis: (Prob 習題 51) y x x 1 = d/2 x 2 = d/2 qq q Q = 1 y rr E1E1 E2E2 E d = vector from q to +q p
Continuous Charge Distributions All charge distributions are ultimately discrete ( mostly protons & electrons ). Continuum approximation: Good for macroscopic bodies. Volume charge density [ C/m 3 ] Surface charge density [ C/m 2 ] Line charge density [ C/m ]
Example 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
Example 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. By symmetry, E has only y- component. Perpendicular to an infinite wire y x dq x P y rr dE dq dE y
20.5. Matter in Electric Fields Point Charges in Electric Fields Newton’s 2 nd law (point charge in field E) Trajectory determined by charge-to-mass ratio q/m. Uniform field between charged plates (capacitors). Constant E constant a. E.g., CRT, inkjet printer, ….
Example Electrostatic Analyzer Two curved metal plates establish a field of strength E = E 0 ( b/r ), where E 0 & 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. For a uniform circular motion: Too fast, hits outer wall Too slow, hits inner wall
GOT IT? An electron, a proton, a deuteron (1p, 1n), a 3 He nucleus (2p, 1n), a 4 He nucleus (2p, 2n), a 13 C nucleus (6p, 7n), & an 16 O nucleus (8 p, 8 n) all find themselves in the same electric field. Rank order their accelerations from lowest to highest assuming 1.p & n have the same mass. 2.The mass of a composite particle is the sum of the masses of its constituents. Ans: 13 C, ( 16 O, 4 He, deuteron), 3 He, p, e. ep 2H2H 3 He 4 HeC 1316 O q/m 18001/11/22/32/46/138/16
Dipoles in Electric Fields Uniform E: Total force: Torque about center of dipole: Work done by E to rotate dipole :t // tangent Potential energy of dipole in E ( i = /2) ( U = 0 for p E ) = dipole moment
Non-uniform field: Total force: Example: dipole-dipole interaction c.f. Van der Waals interaction, long range part. | F | > | F + | Force on end of B is stronger; hence net force is toward A
Application: Microwave Cooking & Liquid Crystals Liquid Crystal Display (LCD) Microwave oven: GHz EM field vibrates (dipolar) H 2 O molecules in food heats up. dipolar molecules aligned but positions irregular
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)
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. Induced dipole Alignment of intrinsic dipoles. internal field from dipoles