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Understanding Electric and Gravitational Potential Energy in Electric Fields

This overview explores the concepts of electric and gravitational potential energy, emphasizing their definitions, calculations, and relationships in electric fields. Electric potential (V) is defined as work per unit charge (V = UE/q), measured in volts (J/C), while gravitational potential energy (PE) relates to the mass in gravitational fields. The study discusses how differences in potential can lead to kinetic energy changes and calculations for particles like electrons accelerated through high voltages. It further elaborates on uniform electric fields and the potential of point charges.

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Understanding Electric and Gravitational Potential Energy in Electric Fields

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  1. Electric Potential

  2. Gravitational Potential gravitational potential energy (work) per unit of mass

  3. high PE low PE + + + + + + - - - - - - q + gain in KE = loss of PE PE depends on charge q

  4. Electric potential = potential energy (work) per unit of charge V = UE/q = volts J/C units: only differences of potential (voltages) are measurable

  5. If define V = 0 @ infinity, then can designate V at a point Work to move a charge (q) from infinity (a great distance) to a given point: W = UE = qV

  6. 5000 V - - - + + + e- electron accelerated through 5000 V -8.01 x 10-16 J ΔPE: speed: 4.20 x 107 m/s

  7. Energy Units S.I. unit: Joule UE = qV 1 J = (1 C) ( 1 V) electron volt (eV): charge of 1 e- across a potential difference of 1 V 1 eV = (1 e-) (1 V)

  8. 1 eV = (1.602 x 10-19 C) (1 V) = 1.602 x 10-19 J 5000 V - - - + + + 2e- energy = 10 000 eV

  9. Q KE: QV - - - + + + m v: √(2QV/m) V 2Q KE: 2QV 2m v: √(2QV/m)

  10. Uniform Electric Field Field strength (+force) is constant

  11. Relationship between V and E for a Uniform Electric Field (between charged plates) W = Fd F = Eq qV W = UE = E = V/d qV = Eqd V/m units: N/C =

  12. E = V/d V = V2 – V1 V2 L ·P r V1 Electric field @ P? Electric potential @ P?

  13. Electric Potential around a Point Charge +Q r X V = kQ/r UE = Vq = kQq/r

  14. If more than 1 point charge: find V for each (include sign) and then find algebraic sum V = k Σi (qi/ri)

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