Physics 1220/1320

1. Electromagnetism – part one: electrostatics Physics 1220/1320 Lecture Electricity, chapter 21-26

2. Electricity • Consider a force like gravity but a billion-billion-billion-billion times stronger And with two kinds of active matter: electrons and protons And one kind of neutral matter: neutrons

3. The phenomenon of charge Problem Invisibility Common problem in physics: have to believe in invisible stuff and find ways to demonstrate its existence. Danger of sth invisible If we rub electrons onto the plastic, is it feasible to say that we rub protons on it in the second experiment? No! If we move protons, we move electrons with them. But what if in the second experiment we still moved electrons – in the other direction?

4. Why matter is usually electrically neutral: • Like charges repel, unlike charges attract • Mixed + and – are pulled together by enormous attraction • These huge forces balance each other almost out so that matter is neutral • Two important laws: Conservation & quantization of charge

5. Where do the charges come from? Electrons and protons carry charge. Neutrons don’t. Positive (proton), negative (electron) Consider: Why does the electron not fall into the nucleus? Why does the nucleus not fly apart? Why does the electron not fly apart? Consequence of QM uncertainty relation More forces, total of four Short ranged – limit for nucleus size Uranium almost ready to fly apart

6. Electric Properties of Matter (I) • Materials which conduct electricity well are called ______________ • Materials which prohibited the flow of electricity are called ________________ • ‘_____’ or ‘______’ is a conductor with an infinite reservoir of charge • ____________ are in between and can be conveniently ‘switched’ • _____________are ideal conductors without losses

7. Induction - Appears visibly in conductors • Induction : Conductors and Insulators • Are charges • present? b) Why are there not more ‘-’ charges? c) Why do like charges collect at opposite side? d) Why does the metal sphere not stay charged forever?

8. Coulomb’s Law • Concept of point charges • Applies strictly in vacuum although in air deviations are small • Applies for charges at rest (electrostatics) Force on a charge by other charges ~ ___________ ~ ___________ ~ ___________ Significant constants: e = 1.602176462(63) 10-19C i.e. even nC extremely good statistics (SI) 1/4pe0 Modern Physics: why value? how constant?

9. Principle of superposition of forces: If more than one charge exerts a force on a target charge, how do the forces combine? Find F1 Luckily, they add as vector sums! Consider charges q1, q2, and Q: F1 on Q acc. to Coulomb’s law Component F1x of F1 in x: What changes when F2(Q) is determined? What changes when q1 is negative?

10. Electric Fields How does the force ‘migrate’ to be felt by the other charge? : Concept of fields

12. Charges –q and 4q are placed as shown. Of the five positions indicated at 1-far left, 2 – ¼ distance, 3 – middle, 4 – ¾ distance and 5 – same distance off to the right, the position at which E is zero is: 1, 2, 3, 4, 5

13. Group task: Find force of all combinations of distances and charge arrangements

14. Group task: Find fields for all combinations of distances and charge arrangements at all charge positions.

15. Direction E at black point equidistant from chargesis indicated by a vector. It shows that:a) A and B are + b) A and B are - c) A + B –d) A – B + e) A = 0 B -

16. Electric field lines For the visualization of electric fields, the concept of field lines is used.

17. Electric Dipoles H2O : O2- (ion) H1+ H1+

18. Gauss’s Law, Flux

20. Group Task: Find flux through each surface for q = 30° and total flux through cube What changes for case b? n1: n2: n3: n4: n5,n6:

21. Gauss’s Law Basic message:

22. Important Applications of Gauss’s Law

23. Group Task 2q on inner 4q on outer shell http://www.falstad.com/vector3de/

24. http://www.cco.caltech.edu/~phys1/java/phys1/EField/EField.htmlhttp://www.cco.caltech.edu/~phys1/java/phys1/EField/EField.html http://www.falstad.com/vector3de/

25. Group Task For charges 1 = +q, 2 = -q, 3= +2q Find the flux through the surfaces S1-S5

26. Electric Potential Energy

28. Electric Potential V units volt: [V] = [J/C]

29. Potential Difference Potential difference: [V/m]

30. Calculating velocities from potential differences Dust particle m= 5 10-9 [kg], charge q0 = 2nC Energy conservation: Ka+Ua = Kb+Ub

31. Outside sphere: V = k q/r Surface sphere: V = k q/R Inside sphere:

32. Equipotential Surfaces

34. Potential Gradient

35. Moving charges: Electric Current • Path of moving charges: circuit • Transporting energy • Current http://math.furman.edu/~dcs/java/rw.html Random walk does not mean ‘no progression’ Random motion fast: 106m/s Drift speed slow: 10-4m/s e- typically moves only few cm Positive current direction:= direction flow + charge

36. Current through A:= dQ/dt charge through A per unit time Work done by E on moving charges  heat (average vibrational energy increased i.e. temperature) Unit [A] ‘Ampere’ [A] = [C/s] Current and current density do not depend on sign of charge  Replace q by /q/ Concentration of charges n [m-3] , all move with vd, in dt moves vddt, volume Avddt, number of particles in volume n Avddt What is charge that flows out of volume?

37. Resistivity and Resistance Properties of material matter too: For metals, at T = const. J= nqvd ~ E Proportionality constant r is resistivityr = E/JOhm’s law Reciprocal of r is conductivity Unit r: [Wm] ‘Ohm’ = [(V/m) / (A/m2)] = [Vm/A]

38. Types of resistivity

39. Resistance Ask for total current in and potential at ends of conductor: Relate value of current to Potential difference between ends. • For uniform J,E • I = JA and V =EL • with Ohm’s law E=rJ • V/L = rI/A Const. r I ~ V ‘resistance’ R = V/I [W] • vs. R R =rL/A R = V/I V = R I I = V/R

41. Group Task E, V, R of a wire Typical wire: copper, rCu = 1.72 x 10-8 Wm cross sectional area of 1mm diameter wire is 8.2x10-7 m-2 current a) 1A b) 1kA for points a) 1mm b) 1m c) 100m apart E = rJ = rI/A = V/m (a) V/m (b) V = EL = mV (a), mV (b), V (c) R = V/I = V/ A = W

42. Resistance of hollow cylinder length L, inner and outer radii a and b Current flow radially! Not lengthwise! Cross section is not constant: 2paL to 2pbL  find resistance of thin shell, then integrate Area shell: 2prL with current path dr and resistance dR between surfaces dR= rdr/(2prL)  dV = I dR to overcome And Vtot= SdV R = int(dR) = r/(2pL) intab(dr/r) = r/(2pL) ln(b/a)

43. Electromotive Force Steady currents require circuits: closed loops of conducting material otherwise current dies down after short time Charges which do a full loop must have unchanged potential energy Resistance always reduces U A part of circuit is needed which increases U again This is done by the emf. Note that it is NOT a force but a potential! First, we consider ideal sources (emf) : Vab = E = IR

44. I is not used up while flowing from + to – I is the same everywhere in the circuit Emf can be battery (chemical), photovoltaic (sun energy/chemical), from other circuit (electrical), every unit which can create em energy EMF sources usually possess Internal Resistance. Then, Vab = E – Ir and I = E/(R+r)

45. Circuit Diagrams (Ideal wires and am-meters have Zero resistance) No I through voltmeter (infinite R) … i.e. no current at all Voltage is always measured in parallel, amps in series

46. Energy and Power in Circuits Rate of conversion to electric energy: EI, rate of dissipation I2r – difference = power output source

47. Resistor networks Careful: opposite to capacitor series/parallel rules!

48. Combining Measuring Instruments

49. Group Task: Find Req and I and V across /through each resistor!

50. Group task: Find I25 and I20