Physics 121 - Electricity and Magnetism Lecture 2 - Electric Charge Y&F Chapter 21, Sec. 1 - 3

1. Physics 121 - Electricity and MagnetismLecture 2 - Electric Charge Y&F Chapter 21, Sec. 1 - 3 • Historical Introduction • Electric Charge • Quantization of Charge • Structure of Matter • Conservation of Charge • Conductors and Insulators • Coulomb’s Law – Force • Shell Theorem • Examples • Summary

2. Electromagnetism is about “Charge”Some History • Static electricity and natural magnets • Rub amber (electron), balloons, comb & paper • Lodestone, near volcanos and meteors • Shocks from door knobs, pipes,… • Van de Graaf generator • 17th Century: (Newton) • Action at a distance “field” concept for gravitation • 18th Century: (Ben Franklin) • Two flavors of “Electric Fluid” (+ & -) • Lightning is electrical • 19th Century: • Currents create magnetic fields (Ampere) & deflect compass needles (Oersted 1820) • Changing magnetic fields produce electric fields (Faraday generator principle - Induction) • Action-at-a-distance “fields” adopted to represent E&M. • Maxwell’s Equations unify Electricity & Magnetism (James Clerk Maxwell, ~ 1865) • Electromagnetic waves are inter-linked, oscillating electric and magnetic fields • Accelerated (e.g., vibrating) charges cause electromagnetic radiation • Electromagnetic (radio) waves actually created in lab using LC circuit (Hertz, 1887) • EM SPECTRUM: Radio, Infra-red, Visible light ,Ultra-violet, X-Rays, Gamma rays • EM waves also behave like particles (photons, E = hf) ELECTRIC & MAGNETIC EFFECTS ARE INTERCONNECTED

3. CHARGED INSULATING ROD ATTRACTS NEUTRAL CONDUCTOR BY INDUCTION. + + + + + + + + + + + + + + + + + + + + + + + + - - - - - - - - F - F CHARGES WITH SAME SIGN REPEL F - - - + + + copper - F CHARGES WITH OPPOSITE SIGN ATTRACT - F F WHAT’S CHARGE? WEAK CHARGE IS A BASIC ATTRIBUTE OF MATTER, LIKE MASS • mass = measures of response to gravitational field and source strength of gravitational field • charge = measures response to electromagnetic field and source strength of electrostatic (electromagnetic) field STRONG • HOW TO GENERATE STATIC CHARGE • Rub glass rod (+) with silk (-)  • Rub plastic rod (-) with fur (+)  • Feet on nylon carpet + dry weather  sparks • Van de Graaf Generator

4. ALL MATTER IS ELECTRICAL …BUT we normally don’t see that? • Matter is normally electrically neutral (equal numbers of + and – charges) • Screening hides most effects of internal charges LARGE OBJECTS GET NET CHARGE BY LOSING OR GAINING BASIC CHARGES • Net + charge  deficit of electrons (excess of “holes”) • Net –charge  excess electrons (deficit of “holes”). • Why can large objects have durable shapes? Electrical forces hold matter together. • Outside neutral atoms electrical forces are “screened”, but not completely. • Weak “leftover” Van der Waal’s force makes atoms stick together & defines properties of solids, liquids, and gases. • Can matter can be neutral everywhere in the universe? Seemingly, yes. • CHARGE IS “CONSERVED”… • …as are ENERGY, MOMENTUM, ANGULAR MOMENTUM, MASS* • Net charge never just disappears or appears from nowhere. • A charge’s effects can be screened out (cancelled) by charge of opposite sign. • Chemical reactions conserve charge while exchanging electrons among molecules. • Nuclear reactions conserve charge but may not conserve mass (E = mc2), e.g.: • radioactive decay: 92U238  90Th234 + 2He4 + energy • pair production & annihilation: g  e- + e+ (electron – positron pair)

5. Electron Proton 2-1: Which type of charge is easiest to pull out of an atom? • Proton • Electron The protons all repel each other Why don’t nuclei all fly apart? Neutron WHAT”S WRONG WITH THIS PICTURE? The solid-seeming physical world we perceive is illusion. Matter is empty space with charged particles • MODERN ATOMIC PHYSICS (1900 – 1932): Rutherford, Bohr • Charge is quantized: e = 1.6x10-19 coulombs (small). • Every charge is an exact multiple of +/- e. ( Milliken ~1900 ). • Electrons ( -e) are in stable orbital clouds with radius ~ 10-10 m., • mass me = 9.1x10-31 kg. (small). Atoms are mostly space. • Protons ( +e) are in a small nucleus, r ~10-15 m , mp= 1.67x10-27 kg, • Ze = nuclear charge, Z = atomic number. There are neutrons too. • A neutral atom has equal # of electrons and protons. • A + or - ion will attract opposite charges to become neutral.

6. induced charge induced charge net charge What’s the Difference between Insulators & Conductors? • Insulators: • Charge remains localized - not free to move • away from being bound to ion • But Material polarizes (not shown) • Conductors: • Charge free to move in a conduction band • Screening effect for charged impurity • Charge separation induced in copper rod • F always attractive for plastic rod • near either end of copper rod • What if plastic rod touches copper rod?

7. - - - - + + + + + + + + + + + + + + + + + + + + + + + + - - - - - - - - LIQUID or GASEOUS CONDUCTOR • Stripped electrons and ions • both free to move independently • Normally in random motion when • there is zero external field • Electrons & ions move in opposite • directions in an E field. - - - - - - - - sea water, humans, hot plasmas - - - - • Conductors: • Weakly bound charges are free to move away from ions • (conduction band states overlap a lot) • Tightly bound electrons are in localized orbital states • (valence band states overlap only a little) SOLID CONDUCTOR • Regular lattice of fixed + ions • Outer electrons form conduction • band & wander, especially when • E-field is applied metals for example

8. Example: Use induction to charge a conducting sphere ground wire 5. + + + uniform distribution 3. 1. 2. + + + - + - + + + + + - draw off negative charge neutral induce charges - - - - - - - - - 4. - - - - - - - - - remove wire

9. Charged rod and aluminum can Chapter 21 Demonstration Source: Pearson Study Area - VTD Discussion: • What type of material was the can made of? • Why did the can roll rather than slide? • Why did the can also roll to the left when the oppositely charged rod was brought near? https://mediaplayer.pearsoncmg.com/assets/secs-vtd32_chargepropelled

10. - - - - + + + + Polarization means charge separates but does not leave home in an atom or molecule Molecules can have permanent polarization...or they may be induced to distort when external charge is near + - + free charge free charge - - - - + + + + - - - - + + + + - - - - + + + + - - - - + + + + - - - - + + + + ………. ………. THE DIELECTRIC CONSTANT MEASURES MATERIALS’ ABILITY TO POLARIZE positive polarization charge field inside insulating material is smaller than it would be in vacuum negative polarization charge Insulators: Charges not free to wander Outer electrons are tightly bound to ions, which can distort... ...Nearby external charges cause “polarization” …Insulators can be solids, liquids, or gases

11. 2-3: Balls A, B, and D are plastic with net charge on them. Ball C is metal and has zero net charge on it. The forces between pairs 1, 2, 3 are as shown. In sketches 4 and 5 are the forces between balls attractive or repulsive? C C Answer choices • 4 is attractive, 5 is repulsive • 4 is attractive, 5 is attractive • 4 is repulsive, 5 is repulsive • 4 is repulsive, 5 is attractive • not enough information D B B D A A D A ? ? 1 2 3 4 5 Insulators and Conductors 2-2: Which of the following are good electrical conductors? • A plastic rod. • A glass rod. • A rock. • A wooden stick. • A metal rod.

12. 3rd law pair of forces along line linking charges F12 q1 r12 q2 F21 Gravitation is weak G m m 1 2 = F Unit of charge = Coulomb 1 Coulomb = charge passing through a wire carrying 1 Ampere of current in 1 second (old) 1 Coulomb = 6.24x1018 electrons [ = 1/e] (new) 12 2 r 12 » - G . x 11 N . m 2 / kg 2 6 67 10 ELECTROSTATIC FORCE LAW (coulomb, 1785) Constant k=8.99x109 Nm2/coul2 Force on q1 due to q2 (magnitude) repulsion shown • Force is between a pair of point charges • An electric field transmits the force • (no contact, action at a distance) • Symmetric in q1 & q2 so F12 = - F21 • Inverse square law • Electrical forces are strong compared to gravitation • e0= 8.85 x 10-12Why this value? Units

13. -2q +Q -q Example: Charges in a Line 2-4: Where should I place charge +Q in order for the forces on it to balance, in the figure at right? • Cannot tell, because + charge value is not given. • Exactly in the middle between the two negative charges. • On the line between the two negative charges, but closer to the -2q charge. • On the line between the two negative charges, but closer to the -q charge. • There is no location that will balance the forces. Can I put Q above -2q or below –q and still have balance?

14. -2q +Q L y -q At what value of y do the forces balance • Sketch forces on Q. • Q is attracted to both negative charges: forces could cancel. • By symmetry, position for +Q in equilibrium is along y-axis • Coordinate system: L is the (fixed) total distance. • y is the (variable) position of charge Q from charge -q. • Net force is sum of the two force vectors, and has to be zero, so • k, q, and Q all cancel due to zero on the left; answer does not depend on knowing the charge values. Result: • Solve for y, , y is less than half-way to the top negative charge

15. 1 proton (in nucleus) & 1 electron in neutral Hydrogen atom • Both particles have charge e = 1.6 x 10-19 C. • me = electron mass = 9.11 x 10-31 kg. • mp = proton mass = 1833 me • a0 = radius of lowest electron orbit = 10-8 cm = 10-10 m. • Electrostatics dominates atomic structure by a factor of ~ 1039 • So why is gravitation important at all? [Matter is normally Neutral!] • Why don’t nuclei with several protons break apart? How do we know that electrostatic force – not the gravitational force - holds atoms & molecules together? Example: Find the ratio of electrical to gravitational forces in Hydrogen atom.

16. force on q1 due to q2 y q1 displacement to q1fromq2 unit vector pointing radially away from q2 at location of q1 q2 x squared cubed COULOMB’S LAW USING VECTORS Sketch shows repulsion: For attraction (opposite charges):

17. y +q2 +q3 x +q1 -q4 Superposition of forces & fields The force between a specific pair of point charges does not depend on interaction with other single nearby charges. “There are no 3-body forces” (same for gravitation). Example: Find NET force on q1 Method: find forces for all pairs of charges that include q1, then add the forces vectorially • Use coulomb’s law to calculate individual pairwise forces • Keep track of direction, usually using unit vectors • Find the vector sum of individual forces at the point • F11 F22 etc, are meaningless • For continuous charge distributions, integrate instead of summing

18. 3 1 2 r23 r12 p e p F12 FBD at 1 F13 F21 FBD at 2 F23 F32 F31 FBD at 3 Example in 1 Dimension: Electron and two protons along a line • Find forces on each charge using Coulomb’s Law. • Construct FBDs (free body diagrams) for # 1, 2, & 3. • By symmetry, all forces are along the horizontal axis • There are 3 action-reaction pairs of forces • Which forces are attractive/repulsive? • Could net force on any individual charge be zero above? • What if r12 = r23?

19. F12 F21 R x q1 q2 Magnitude of force: small! So what! In vector notation: EXAMPLE: Start with two point charges on x-axis Use vector notation for direction of result Find F12 : the force on q1 due to q2 F21 has the same magnitude, opposite direction q1 = +e = +1.6 x 10-19 C q2 = +2e = +3.2 x 10-19 C. R = 0.02 m

20. R F12 F21 r23 r13 x q3 q1 q2 • force is pairwise so F12 & F21 are not affected...BUT... • four new forces appear, having only two distinct new magnitudes. • F13 and F23 .... see FBDs below. F12 done above. R F12 F13 q1 r13 F21 F31 F32 q3 r23 F23 …see next page... q2 EXAMPLE continued: add charge q3 on x-axis between q1 and q2 q3 = - 2e = -3.2 x 10-19 C. r13= ¾ R, r23= ¼ R What changes?

21. Find net forces on each of the three charges by applying superposition On 1: On 2: On 3: EXAMPLE continued: calculate magnitudes

22. a a a a a • Spheres initially attract (induction),then repel. Find force Do the spheres approximate point charges? What about induction? We applied shell theorem anyway. Another Example: Find the final charges after the spheres below touch? B B B -15e +20e What determines how much charge ends up on each? -30e A A A -50e -15e • Example: Charge Movement in Conductors • Two identicalconducting spheres A&B. Radii small compared to a. • Sphere A starts with charge +Q, sphere B is neutral • Connect them by a wire. What happens and why? Charge redistributes until ......??? Why do the final charges become equal? Are they equal if the spheres are not identical? B B B 0 +Q/2 +Q/2 A A A +Q +Q/2 +Q/2

23. Supplementary Material

24. insulator Proof by lengthy integration or symmetry + Gauss Law + + + + + + q r + + P + + R + + + + + + + Outside a shell, r > R: test point charge q feels force indistinguishable from replacing all the shell’s charge with a point charge Q at the center of the shell. Inside a shell, r < R: test charge q inside uniform hollow shell of charge feels zero net electrostatic force from the shell. Why does the shell theorem work? spherical symmetry  cancellations Force on a point charge near an insulating spherecarrying a spherical surface charge distribution. • Apply Shell Theorem (similar to gravitational - see Lecture 1) • Uniform surface charge density s on insulator - not free to move • Holds for spherical symmetry: shell or solid sphere of charge • Shell has radius R, total charge Q

25. q Q Now bring finite test charge q<<Q near the sphere Q is a point charge here q Q 2R d d • The test charge q induces charge separation on the conducting sphere • Charge distribution on sphere will NOT be uniform any more • Extra surface charge is induced on the near and far surfaces • The net force will be slightly more attractive than for point charges The Shell Theorem works approximately for conductors if the test charge induces very little separation; e.g., if q << Q and/or d >> R. Charge on a spherical conductor – charge free to move Isolated system (no other charges nearby or q is tiny ) • Net charge Q on a spherical conducting shell spreads out everywhere over the surface. • Tiny free charges inside the conductor push on the others and move as far apart as they can go. When do they stop moving? • Charges spread themselves out uniformly because of symmetry Sphere acts approximately as if all of it’s charge is concentrated at the center (for points outside the sphere) as in the Shell Theorem.

26. Outer energy levels overlap a lot, so weakly bound electrons can wander conduction band BAND GAP Tightly bound energy levels overlap a little, to support rigid crystal structure or liquid viscosity valence band ENERGY Semiconductor Materials • Normally insulators, but can be weak conductors when • heat, impurity doping, or voltage is applied to electrons • normally in valence states (tightly bound). • Electrons are excited to overlapping higher atomic energy • levels forming conduction band.

27. q1 = + 8q q not stated q2 = -2q qprot = +e y qprot q1 q2 Region III Region I Region II Both forces to the right No equilibrium possible If qprot in Region I: qprot If qprot in Region III: qprot Forces opposed but and Forces can never balance If qprot in Region II: qprot Forces opposed and So balance point exists here L x Find x for equilibrium: Did the test charge magnitude make any difference? Example: point charges q1 & q2 on x-axis In the sketch where could a proton qprot be in equilibrium (Set Fnet = 0, use “free body diagrams” & symmetry)