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Electric Potential

jhardman
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Electric Potential

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  1. Capacitors exist everywhere. Nature has evolved nerve cells of which the axons are capacitors of a sort! By creating a capacitor (cell membrane) and an Electric Field between the surfaces of the cell membrane we are able to store energy in the Electric Field for later use. We transform the energy in the Electric field to energy of motion.  Electric Potential

  2. Work and Energy

  3. Gravitational Work and Energy Work is done against gravity to move the block from A to B, a vertical height h. Work = Fd = mgh A The external force does positive work; the gravity g does negative work. B The external force F against the g-field increases the potential energy. If released the field gives work back.

  4. Electric Potential Energy • Electrical potential energy is the energy contained in a configuration of charges. • Like all potential energies, when it goes up the configuration is less stable; when it goes down, the configuration is more stable. • Electrical potential energy increases when charges are brought into less favorable configurations (ex:, like-sign charges getting closer together, or unlike-sign charges farther apart). ΔU > 0

  5. Electric Potential Energy cont… • Electrical potential energy decreases when charges are brought into more favorable configurations (ex:, like-sign charges getting further apart, or unlike-sign charges closer together). • Work must be done on the charge by an outside force to increase the electric potential energy. ΔU < 0

  6. Work changes potential energy! When an outside force is applied to a positive test charge to move it a distance d, the electric force does negative work. (WE = - FEd) The electric potential energy has increased and U is positive (U2 > U1) If a negative charge moves upward a distance d, the electric force does positive work (WE = +FEd). The change in the electric potential energy U is negative (U2 < U1)

  7. Electrical Potential and Potential Energy • The change in potential energy is directly related to the change in voltage. • U = EPE= qV • U: change in EPE (J - joules) • q: charge moved (C - coulombs) • V: potential difference (V - volts) • All charges will spontaneously go to lower potential energies if they are allowed to move.

  8. ΔU = EPE = qΔV Sample: A 3.0 μC charge is moved through a potential difference of 640 V. What is its potential energy change? = (3 x 10-6 C)(640 V) = 1.92 x 10-3 J

  9. Electrical Potential &Potential Energy • Since all charges try to decrease potential energy, and DU = qDV, this means that spontaneous movement of charges result in negative DU(EPE). • Positive charges like to DECREASE their potential (DV < 0) • Negative charges like to INCREASE their potential. (DV > 0)

  10. Since the electric force is F = qE, the work that the electric force does as the charge moves from A to B depends on the amount of the charge. It is useful to express this work on a per charge basis. WAB = EPEA- EPEB=UEA– UEB = ΔU q qqqq The electric potential or Voltage,Vis defined in terms of the work to be done on a charge to move it against an electric field.

  11. Electric Potential (spherical) • For a spherical or point charge, the electric potential can be calculated • V: potential (V) • k: 9.0 x 109 N m2/C2 • q: charge (C) • r: distance from the charge (m) • Remember, k = 1/(4peo) Substituting for U, we find V:

  12. Sample a. Calculate the potential at a point A that is 30 cm distant from a charge of- 2 μC. Q = - 2 μC r = 0.3 m = - 6x104 V b. Find the potential energy if a +4 nC is placed at point A. q = +4 nC UE= qVA = 4 x10-9C (- 6x104 V) = -2.4x10-4 J A -2μC

  13. An equipotential surface is a surface on which the electrical potential is the same everywhere. The easiest way to see these equipotential surfaces is to picture them around a point charge What happens to the potential as you move away from the point charge?

  14. The electrical potential decreases as you move away from the charged particle. Lines of equal potential are always perpendicularto the electric field lines and point toward decreasing potential. highest lowest

  15. NO WORK is done if a charge moves on an equipotential surface Work is required for a charge to move to a different equipotential surface.

  16. Electrical Potential in Uniform Electric Fields • The electric potential is related in a simple way to a uniform electric field. • V = Ed • V: change in electrical potential (V) • E: Constant electric field strength (N/m or V/m) • d: distance moved (m) ++++++ ------ d Equipotential lines E DV More V Less V

  17. Sample: An electric field is parallel to the x-axis. What is its magnitude and direction if the potential difference between x = 1.0 m & x = 2.5 m is found to be + 900 V? 1.0 2.5 X (m) ΔV = Ed E = ΔV/d = (+ 900 V)/1.5 m = 600 V/m Magnitude is 600 V/m Direction is – X cause ... + 900 V means potential is increasing so field is toward the left (or – x)

  18. Use of conservation of energy… Sample: A proton at rest is released in a uniform electric field. How fast is it moving after it travels through a potential difference of 1200 V? UB +KB = UA + KA qΔV + 0 = 0 + ½ mv2 (1.6 x 10-19C)(1200V) = ½ (1.67 x 10-27kg) v2 1.92 x 10-16 J = ½(1.67 x 10-27kg) v2 480,000 m/s = 4.80 x 10 5 m/s = v

  19. UE is Electric Potential Energy (Joules) and is notVis Electric Potential (Joules/Coulomb)a.k.a Voltage, Potential Difference UE=

  20. ΔV = Ed ΔVBtoA= (400N/m)(2m - 1m)= 400V Sample: What is the voltmeter reading between A and B? Between C and A? Assume that the electric field has a magnitude of 400 N/m. ΔVBtoC= (400N/m)(2m - 2m)= 0V ΔVAtoC= - 400V (decrease in Potential) +++++++ y(m) ------- C 1.0 A B 1.0 2.0 x(m)

  21. UE = qEd= qV UE AtoC= (2.0 x10-3C)(-400V) = -0.8 J way it wants to move How much work would be done BY THE ELECTRIC FIELD in moving a 2 mC charge from A to C? From A to B? from B to C?. How much work would be done by an external force in each case? UEBtoC= (2.0 x10-3C)(0V) = 0 J +++++++ y(m) ------- ΔVBtoC = 0V C 1.0 d A B F ΔVAtoB = 400V 1.0 2.0 x(m) UE BtoA= 0.8 J against the field

  22. Sample: What is the potential energy of the configuration shown below? y (m) 2.0 1.0 2 mC 4 mC x (m) 1.0 2.0

  23. Sample: What is the electric potential at (2,2)? y (m) 2.0 -3 mC 1.0 2 mC 4 mC x (m) 1.0 2.0

  24. Sample: How much work was done in assembling the charge configuration shown below? y (m) 2.0 -3 mC 1.0 2 mC 4 mC x (m) 1.0 2.0

  25. For spherical charges Scalars Vectors Force between Electric Potential energy of Field because of Potential because of

  26. Oppositely Charged Parallel Plates & Uniform Fields: WorkAB = q(VA – VB) Work BY E-field Work = Fd = (qE)d

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