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Electric Potential

Electric Potential. AP Physics B Chapter 17 Notes. E. D V. Electric Potential. Recall gravitational potential energy Work done by gravity in moving object from A to B is equal to the change in GPE W = mgh B −mgh A = GPE B −GPE A. Electric Potential.

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Electric Potential

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  1. Electric Potential AP Physics B Chapter 17 Notes E DV

  2. Electric Potential • Recall gravitational potential energy • Work done by gravity in moving object from A to B is equal to the change in GPE W = mghB−mghA = GPEB −GPEA

  3. Electric Potential An analogous situation for the work done by the electric field on the charge hA hB

  4. Electric Potential • The work done by the electric field going from A to B is equal to the change in electric potential energy W = EPEB −EPEA Note: The electric force is a conservative force just like gravity, so the path taken does not affect W hA hB

  5. Electric Potential • As the charge moves, the work done by E is W = Fd= qEd so EPEB −EPEA = -qEd (For uniform electric field)

  6. Electric Potential DEFINITION OF ELECTRIC POTENTIAL The electric potential at a given point is the electric potential energy of a small test charge divided by the charge itself: (recall for electric field) SI Unit: J/C = V (volt) Note: Be careful not to confuse PE and potential (V)

  7. Electric Potential As with GPE, only differences inpotential between two points are meaningful: V depends on charges that create the field, not on charge in field Positive charge side (of plate) is higher potential

  8. Electric Potential Common Electric Potentials Flashlight battery 1.5 V Car battery 12 V Electrical Outlet (US) 120 V Electrical Outlet (Europe) 240 V Our VDG 400 kV Medium lightening bolt 35 MV

  9. Van de Graaff Generator 1. hollow metallic sphere 2. electrode connected to the sphere 3. upper roller 4. side of the belt with positive charges (going up) 5. opposite side of the belt with negative charges (going down) 6. lower roller (metal) turned by motor 7. lower electrode (ground) 8. spherical device with negative charges 9. spark produced by the difference of potentials

  10. Electric Potential--Example Conceptual Example: A positive test charge is released from A and accelerates towards B. Upon reaching B, the test charge continues to accelerate toward C. Assuming that only motion along the line is possible, what will a negative test charge do when released from rest at B?

  11. Electric Potential We now have another form of energy: Translational Rotational Gravitational Elastic Electric KE KE PE PEPE Another useful unit for energy is electron volt, the energy to move a charge of 1e through 1 V 1 eV = 1.6 x 10-19 J Useful for subatomic particles, but not an SI unit

  12. Electric Potential--Example A particle has a mass of 1.8x10-5kg and a charge of +3.0x10-5C. It is released from point A and accelerates horizontally until it reaches point B. The only force acting on the particle is the electric force, and the electric potential at A is 25V greater than at B. (a) What is the speed of the particle at point B? (b) If the same particle had a negative charge and were released from point B, what would be its speed at A?

  13. Electric Potential and Electric Field The effects of charge distribution can be described in terms of E or V W= -qVba and W= Fd= qEd so Vba = -Ed or E d DV

  14. Electric Potential and Electric Field A pair of oppositely charged, parallel plates are separated by 5.33 mm. A potential difference of 600 V exists between the plates. (a) What is the magnitude of the electric field strength between the plates? (b) What is the magnitude of the force on an electron between the plates?

  15. Equipotential Lines • Equipotental line is one on which all points have the same potential • Equipotential lines are ⊥ to E field lines • Similar to contour lines on a topographical map

  16. Equipotential Lines Electric field lines and equipotential lines for a dipole

  17. Electric Potential of Point Charges Consider a charge q0 being repelled by q from A to B: Potential difference: If rB goes to infinity, VB 0 so

  18. Electric Potential of Point Charges • V approaches zero as r goes to infinity • V from individual charges is additive: Signs on charges must be kept!

  19. Electric Potential of Point Charges • Recall finding E due to multiple charges… magnitude and direction… hassle central! • V from individual charges is additive and we don’t need to worry about direction… easy button!

  20. Electric Potential of Point Charges Find the potential at points A and B. Find the potential at point A.

  21. Electric Potential Summary ∆PE = -qEd Work done by E force *Va=PEa/q Electric potential at point a Vba = Vb-Va = -Wba/q Potential difference *Vba = -Ed V related to uniform E *V = k(Q/r) V due to point charge (can Σ) *PE = k(Q1Q2/r) PE between two charges *On formula page (or variant)

  22. Capacitors • Capacitors store electric charge which can be released as needed • Capacitors have conducting plates separated by an insulator (E field between plates!)

  23. Capacitors If parallel plates are connected to a voltage supply (battery), the plates will become charged Recall ∆V = Ed, so ∆V∝ E E ∝ Q, so Q ∝ ∆V Call C a proportionality const. Q = CV or C=Q/V C is capacitance and has units of farads = F = C/V

  24. Capacitors Capacitance does not depend on voltage but only on geometry and materials: ε0 is vacuum permittivity, a constant of proportionality ε0 = 8.85 x 10-12 C/Nm2

  25. Capacitors Capacitors are used in circuits for a variety of reasons—one of which is to store a large amount of charge to be released almost instantaneously Think camera flash

  26. Capacitors Air is not a great insulator, so this limits the potential that charge can be stored before it starts to flow Insulators are usually used—called dielectrics Reduce E field, V decreases (V=Ed), so C increases for same Q (or more Q for same V)

  27. Capacitors and Storage of Energy The energy stored on a capacitor = W done to charge it V decreases as charge stored, so W=Q(Vf/2) PE = energy = ½(QV) Using Q = CV PE= ½(QV) = ½(CV2) = ½(Q2/C)

  28. Capacitors—Example Problems P 38, pg. 490 If a capacitor has opposite 5.2μC charges and E of 2.0kV/mm is desired between the plates, what must each plate’s area be? How much energy is stored in our camera flash unit (C= 80μF and V = 330V)?

  29. Capacitors—Example Problems A common type of keyboard uses capacitors to recognize key strokes. Each key is mounted to one end of a plunger that is connected to a movable metal plate. The movable metal plate is above a fixed plate and acts as a capacitor. When the key is pressed, d decreases so capacitance increases. The computer can detect this change in capacitance.

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