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18-1 Electric Potential Energy

18-1 Electric Potential Energy. Electric Potential Energy- potential energy associated w/ an object due to its position relative to a source of electric force. ( it is a form of mechanical energy ) * Anytime a charge moves because of an electric force, work is done on that charge. ME=KE + PE

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18-1 Electric Potential Energy

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  1. 18-1 Electric Potential Energy • Electric Potential Energy- potential energy associated w/ an object due to its position relative to a source of electric force. (it is a form of mechanical energy) • *Anytime a charge moves because of an electric force, work is done on that charge. • ME=KE + PE • =KE + PEg + PEelastic + PEelectric • (Mechanical Energy is conserved is the absence of friction and radiation)

  2. Electric Potential energy can be associated w/ a charge in a uniform field • Uniform field – field that has the same value and direction at all points. E A B

  3. Electric Potential energy can be associated w/ a charge in a uniform field • PEelectric = -qE d • The negative sign indicates PE will be + if q is – ( PE will increase) • While PE will be – if q is + (PE will decrease) • PE = PEf – PEi

  4. The difference in electric potential energy is the quantity that is important • So if we choose the initial position to be our reference point then the displacement becomes the distance moved in the direction of the Electric field. (+d if same direction as electric field, -d if opposite direction of electric field) • We also chose the initial potential energy level as zero

  5. Electric Potential Energy in a Uniform Electric Field • PEelectric = -qEd Units, J = 1N*M Electric PE = - (change[+/-])(electric field strength) (displacement from reference point in the direction of the field [+/-]) T) Components do not change PE!)

  6. Electric Potential Energy E (+) 2. (+) charge in the Direction of electric field cause PE to decrease • Do work to force • Together move (+) • Charge in direction • opposite the field causes • the electric PE to increase

  7. Electric Potential Energy E (+) • Do work to pull • them apart. PE • increases as (-) moves • in direction of the field. 2. PE decreases as (-) charge moves opposite the field.

  8. Gravitational PE PE = + (do work) Neg. work (easy, object wants to return to PE=0) PE = 0 PE = - Earth Earth

  9. Electric Potential Energy Associated with a Pair of Charges • Recall that a single point charge produces a NON-UNIFORM ELECTRIC FIELD (in varies in direction and magnitude depending on the position relative to the charge)

  10. If a second charge is nearby, there will be electric potential energy associated with the 2 charges. Assumptions: 1. reference point for electric PE is 0 at infinity 2. Because like charges repel, + work must be done to bring them together (PE electric is + for like charges and – for unlike charges)

  11. Since like charges attract, bringing them together will reduce the electric potential (-) Since unlike charge repel, work would need to be done by an outside source to bring the charges together, hence increasing the electric potential (+)

  12. Include the signs of the charges, if PE is + that indicates that the PE increases as the charges are brought together from infinity (work has to be done for this to happen) • If PE is – then PE decreases as the electrons are brought together, since this occurs due to the interaction of charges, the charges themselves are said to do the work.

  13. 18-2 Potential Difference • Electric Potential – the electrical potential energy associated with a charged particle divided by the charge of the particle • Since PEelectrical is proportional to q therefore as q , PE . Electric Potential is a more practical concept to study • Electric Potential @ a point is independent of the charge as that point PEelectric V = q

  14. Example #1 • The electric potential energy associated w/ an electron & a proton is -4.35x10^ -18 J. What is the distance between these 2 charges? Given: q1 = 1.6x10^-19 C q2 = -1.6x10^-19 C PEe = -4.35x10^-18 J Find: r Kc q1q2 (8.99x10^9)(-1.6x10^-19)(1.6x10^-19 (-4.35x10^-18) R = Equation: PEe = r R = 5.29x10^-11

  15. Potential Difference • Potential Difference – the change in electric potential energy associated w/ a charged particle divided by the charge of the particle. • Potential difference between 2 terminals of a battery range from 1.5v 12v (car battery) • Potential difference between 2 slots in household electric outlet is about 120v. PEelectric q Units, 1 volt V = J/C V =

  16. Potential difference in a uniform field • Varies w/ the displacement from a reference point PEelec = -qEd PEelec = -qE d V = -qE d q V = -E d Potential diff = -( magnitude of electric field) *(displacement) Moved in direction of field

  17. Potential Difference • The reference point for potential difference near a point charge is often at infinity. • To determine the potential difference between 2 points in the field of a point charge, we 1st calculate the electric potential associated with each point b r q1 a q2

  18. Potential Difference • Imagine a pt. Charge q2 in the electric field of pt charge q1 • Electric Potential @ pt. A due to q1 • Note: the charge q1 is responsible for the electric potential at point a, therefore as electric potential exists at some point regardless of whether there is a charge at that point V = PEelec = Kc q1q2 q2 r q2 Electric Potential @ Pt. a depends on the charge at pt. b & the distance r. V = Kc q1 r

  19. Potential Difference • To determine the potential difference between any two points near pt. Charge q1 (if the distances are r1 & r2 • If distance r1 is large enough it is assumed to be at infinity V = Kc q1 Kc q1 r2 r1 V = Kc q1 1 1 r2 r1 1 r 0

  20. Potential Difference V = Kc q1 r2 Dropping subscripts V = Kc q r Value of point charge Distance to pt. charge Pot. Diff = coulomb constant x

  21. Electric Potential • Total Electric potential = algebraic sum of electric Potentials. • (electric potential is scalar so no vector is needed) • *electric potential is + or – • So sometimes they “add” or sometimes they “subtract”

  22. Batteries • A battery does work to move charges conductors V = 12v + - 12v higher then - terminal Battery Light bulb Assume grounded (–) terminal ; it has an electric potential of 0v

  23. Batteries Each 1 C Charge gives Up 12 J of Electric potential Energy to External devices V=12v=PE q This means that every coulomb of positive charge that leaves the + terminal has 12J of electric potential energy + - Electric Potential is now zero again at the - terminal

  24. 18-3 Capacitance • Capacitor- device used in electric circuits to store charge and energy that is available to be used for a specific application • When used in a circuit, the plates are connected to the 2 terminals of a battery or other potential difference. 2 parallel metal plates separated by a small distance } Typical design

  25. Capacitance + + + Before charging no net charge on plates Small net charge on each plate Greater net charge on each plate after charging Charging stops when potential difference between the plates is equal To potential difference between the terminals

  26. Capacitance • Capacitance- the ability of a conductor to store energy in the form of electrically separated charges. • Defined as the ratio of • Capacitance, C Net charge on each plate Potential difference Q V 1C volt C= 1F = Units,farad,F Typical capacitors range from 1pF 1MF

  27. Capacitance • Capacitance depends on the size & shape of the capacitor • Parallel – plate capacitor w/ no material between its plates (in a vacuum) Notice- the amount of charge that a ll-plate capacitor can store for a given potential difference increases as the plate area increases Area of 1 of the plates A d C= E Distance between the plates Permittivity of a medium between plates C^2 N*m^2 Also: C as d E = 8.85x10^-12

  28. Capacitance • The material between the plates of a capacitor can change its capacitance. • (our prior formula assumes nothing between plates (vacuum)) • Many ll-plate capacitors, the space is filled w/ a material called a dielectric Insulating material ex: rubber, glass, waxed paper More chare can be stored on each plate for a given potential difference

  29. Capacitance • Discharging Capacitors: once a capacitor is charged, the battery (or other source of potential difference) can be removed from the circuit. • The 2 plates will remain charged unless they are connected with a material that conducts • Once the plates are connected the capacitor will discharge Ex: device that uses a capacitor flash attachment ofa camera

  30. Electric potential Energy Stored in a Charged Capacitor PEelec = ½ Q V

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