Lecture 10

# Lecture 10 - PEP112 Spring 2008 Prof. Svetlana Malinovskaya...

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PEP112 – Spring 2008 Prof. Svetlana Malinovskaya 19 February 2008 The Electric Potential Energy

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The Electric Force The electric field between the parallel plates of a capacitor is uniform. We define a coordinate axis s from the negative plate toward the positive plate. A positive charge q speeds up and gains kinetic energy as it moves toward the negative plate. The capacitor+particle’s mechanical energy is conserved. Thus charge loses potential energy as it gains the kinetic one. We calculate potential energy from work. The electric force is a conservative force, the work done by a conservative force is independent on the path followed. cos0 ( ) el i f F qE WF r q E s s qEs qEs = = =
The work done by the electric field causes the charge to experience a change in electric potential energy. 0 cos0 ( ) el i f if elec f i el el F qE WF r q E s s qEs qEs UU U W q E s = = = Δ= = =+ The Electric Potential Energy s is a distance from the negative plate, U 0 is the potential energy at the negative plate.

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Conservation of energy inside a capacitor A 2x2 cm capacitor has spacing 2 mm. First a proton, then electron is released from the midpoint. What is each particle’s change in potential energy? What is each particle’s speed as it reaches the plate? () 00 1 0 22 pf i d UUU U U e E e E d ⎛⎞ Δ= = + + = ⎜⎟ ⎝⎠ 1 efi d U U U U eE d U d −= + + =
17 2 2 5 6 4.52 10 0 1 0 2 1 2 2.33 10 m/s for the proton 2 9.96 10 m/s for the electron pe ff

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## Lecture 10 - PEP112 Spring 2008 Prof. Svetlana Malinovskaya...

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