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Exam Review I

Exam Review I. Physics 208. Chapters 23-28. Coulomb force between charges Work done to move a charge Electric potential as  U/q Electric field as F/q Motion of charged particle in electric field Relation between electric field and electric potential

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Exam Review I

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  1. Exam Review I Physics 208

  2. Chapters 23-28 • Coulomb force between charges • Work done to move a charge • Electric potential as U/q • Electric field as F/q • Motion of charged particle in electric field • Relation between electric field and electric potential • Electric field lines and equipotentials • Electric fields in and near conductors • Electric flux and Gauss' law • Electric field and potential of a point charge, line charge, sheet charge, spherical shell • Capacitance of an isolated conductor, and of a pair of conductors • Calculating capacitance, parallel plate, cylinder, sphere • Energy in a capacitor, energy density, energy in E-field • Dielectrics • Current and resistance, Ohms law • Power dissipation in a resistor • Simple circuits (parallel and series) and RC circuits

  3. - + + - - - + + + + + + + + + + + + + + + - electron flow + + Positively charged metal + + + + + + + + + + Less positively charged rod Charging processes • Conduction • Induction Triboelectric: glass rod rubbed with silk  positive rubber rod rubbed with fur  negative

  4. Quiz on Charge Conservation If you rub an inflated balloon against your hair, the two materials attract each other, as shown in this figure. Fill in the blank: the amount of charge present in the system of the balloon and your hair after rubbing is _____ the amount of charge present before rubbing. (a) less than (b) the same as (c) more than

  5. Quiz on charge sign 1 2 3 1 2 3 1 2 3 - + - + - + - + + 3 pithballs suspended from thin threads are charged by touching them with a charged object. It is found that pithballs 1 and 2 repel each other and pithballs 2 and 3 repel each other. Which of the following statements are correct? 1 and 3 carry opposite charge All of them carry charges of the same sign We need to do more experiments to determine the sign of the charges

  6. Quiz on charge sign cont. A B C A B C - + + - - + 3 objects are brought close to each other, 2 at a time. When objects A and B are brought together, they attract. When objects B and C are brought together, they repel. From this, we conclude that: (a) objects A and C possess charges of opposite sign. (b) all three of the objects possess charges of the same sign. (c)we need to perform additional experiments to determine information about the charges on the objects.

  7. Answer Answer: (c). In the first experiment, objects A and B may have charges with opposite signs, or one of the objects may be neutral since they can attract one the other even due to induction. The second experiment shows that B and C have charges with the same signs, so that B must be charged. But we still do not know if A is charged or neutral.

  8. Insulators and conductors One of these isolated charged spheres is copper and the other is rubber. Label which is which and support your answer with an explanation. a) A is rubber and B is copper. b) A is copper and B rubber c) They are both copper Charged rubber rods are placed near a neutral conducting sphere, causing a redistribution of charge on the spheres. Which of the diagrams below depict the proper distribution of charge on the spheres? List all that apply. A and D C and B E

  9. Coulomb’s Law • Electrical force between two stationary charged particles • The SI unit of charge is the coulomb (C ), µC = 10-6 C • 1 C corresponds to 6.24 x 1018 electrons or protons • ke = Coulomb constant ≈ 9 x 109 N.m2/C2 = 1/(4πeo) • eo permittivity of free space = 8.854 x 10-12 C2 / N.m2

  10. Electric Force

  11. Electric Force magnitude The electric force between 2 like charged objects is F=0.02 N. If the charge of one of the 2 objects is halved and the distance separating the 2 objects is doubled, what is the new force?

  12. Electric Force: Newton’s 3rd law

  13. Forces as vectors F2 F1 + 2 small beads with positive charges +3q and +q are fixed at the opposite ends of an horizontal rod. A 3rd small charged bead is free to slide on the rod. a) Does the result depend on the sign of the charge on the bead? b) Find its equilibrium position. The result is independent on the sign of the charge of the bead Equations to solve the problem (q’ charge of the bead): d2 d1 1 2 F1 F2 -

  14. Electrostatic Potential of 2 like charges

  15. E field, potential difference and energy conservation - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + ++ An electron initially travels horizontally in a uniform electric field pointing upwards with 3 possible directions of the initial velocity of the same magnitude. Which of the following relation is correct? a) vb > v > va b) va > v > vb c) vb = va > v d) vb = v = va Answer: a) the greatest change in potential V occurs for the case with the max vertical deflection from the initial position. This occurs when the electron is projected at an angle below the horizontal. x b L a K = -U=-qV

  16. Example E Fields and Potential  What is the electric field at point B? y B x d2=4 m d +12 C -12 C A - + What is the electric field at point A? d1=3 m 3 m 3 m Calculate the force on a Q=-3mC charge placed at point A: F=QE

  17. Example E Potential y Calculate the electric potential at B B x d d2=4 m -12 C +12 C A - + Calculate the electric potential at A d1=3 m 3 m 3 m Calculate the work YOU must do to move a Q=+5 mC charge from A to B.

  18. Gauss’ Law

  19. Electric Flux

  20. Plane charge density The electric charge density for plate 1 is - and for plate 2 is +The magnitude of the electric field associated with plate 1 is: /(20) and the filed lines are shown in the figure. When they are placed parallel one to the other, the Magnitude of the field is: 1. /0 between and ± /(20) outside 2. /0 between and 0 outside 3. None of the above

  21. Insulator and Conductor sphere inside the insulating shell uniform charge distribution A solid nonconductive spherical ball of diameter d = 2R = 1.0 cm is uniformly charged such that is has an electric field of 20 kV/m at its surface. How much charge is on the ball? Chose gauss surface with r = R 2. What is the magnitude of the electric field halfway to the center of the ball? 3. If the ball were made of a conductive material, how would the answers to 1) and 2) change? R 1. Same (all charge on surface) 2. E = 0 (field inside a conductor is 0)

  22. Capacitors • C  Q/V • Parallel Plate C = e0A/d • Adding • Series • Veq=V1+V2 • Qeq = Q1=Q2 • Parallel • Veq=V1=V2 • Qeq = Q1+Q2

  23. Energy stored in a parallel plate capacitor The parallel plates of a capacitor with vacuum between them are given equal and opposite charge. If the plates are pushed closer from a distance d to D < d, does the energy stored in the capacitor Increase Decrease Remain equal

  24. Metal slab in a capacitor In the slab E = 0 and we have 2 equivalent capacitors in series In the other case the capacitance between the 2 bottom plates is (for the other 2 plates at the same potential 1/C 0)

  25. Capacitor with slab of dielectric A dielectric slab is introduced between the plates of a capacitor. The capacitor is charged and then the dielectric is removed. Which of the following statements are correct: The stored energy increases The capacitance increases The potential difference decreases 0 = quantities in vacuum

  26. Calculate the equivalent Capacitance C1 C2 C3 V C4 parallel C1, C23, C4 in series C1 = 10 mF C2 = 20 mF C3 = 30 mF C4 = 40 mF V = 50 Volts Compare V1 with V4 C1<C4V1>V4

  27. Resistors • R = V/I • R= rL/A • P = RI2 • Adding • Series • Veq=V1+V2 • Ieq = I1=I2 • Parallel • Veq=V1=V2 • Ieq = I1+I2

  28. Resistors in Series

  29. Resistors in Parallel

  30. Light bulbs in Series Consider the resistance of the wire negligible Since the wire has R =0 all current will flow through it and bulb B will fade. Instead A will look brigther since the current in A increaseas from I = V/(RA+RB) to I = V/RA

  31. Light Bulbs of Different Power in Parallel A 100 W B 60 W Which of the following statements are correct? A looks dimmer than B A looks as bright as B A looks brighter than B RA < RB more current flows in A: IA>IB RAIA2 > RBIB2 What happens if A and B are connected in series?

  32. Resistors in series and parallel

  33. Kirchhoff’s Rules - I1 = I2 + I3 • Junction Rule: S Iin = S Iout • A statement of Conservation of Charge • Loop Rule: • A statement of Conservation of Energy

  34. Kirchhoff’s laws R1 = 10 W R2 = 20 W R3 = 30 W V1 = 50 Volts V2 = 10 Volts 2 loops Chose 2 currents and their verse V2 - + R1 I1 I2 +- R2 R3 V1 Calculate total power delivered by the batteries

  35. RC Circuits: CHARGE OF C R Calculate current immediately after switch is closed. C  I = /R = 2 A S1 Calculate current after switch has been closed for 2 time constants R=10, C=30 mF and =20 Volts =RC = 0.3 s Calculate current after switch has been closed for a very long time Calculate charge on capacitor after switch has been closed for a long time

  36. RC Circuits You are given a 5-pack of R=2W resistors and a 5-pack of C=2mF capacitors. How do you configure them to produce a circuit of 21 ms time constant RC circuit? Time constant, t = RC = 21 ms = 7 * 3 ms = 7 W * 3 mF

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