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Ch 23 Electric Potential_2009

# Ch 23 Electric Potential_2009 - Electric Potential Ch 23 In...

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Electric Potential Ch 23 In mechanics, the idea of work and energy made a number of difficult problems much easier to solve. For example the work it takes to push a box across a titled floor with friction. In this chapter we combine the development of work and energy of mechanics with electrical force, charge and electric fields .

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Electric Potential Energy Recall for mechanical systems work done by a force F between points a and b was defined to be: = = b a b a dr F r d F W cos φ dr is an infinitesimal displacement along the particle’s path and φ is the angle between F and dr.
If the force is conservative, ( does not depend on time; only on displacement ), then the work done by F can be expressed in terms of potential energy U . Friction is a non-conservative force; gravity is a conservative force. U E K W - = = . . Work energy theorem extended into the negative of the change of the potential energy: f f i i K U W K U + = + + Conservation of Energy principle with work. F k z U j y U i x U U = + + = - ˆ ˆ ˆ

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Electric Potential Energy in a Uniform Field Let us consider the work done on a test charge q 0 (always positive and small). As the charge is moved from point a to point b , the force acting on the charge is constant (because the electric field was shown to be between two charged plates) and F e = q 0 E Ed q Fd W 0 = = The work done on the charge by the constant force F over distance d is:
Ed q Fd W 0 = = This is the electrical work. In form is exactly like the work gravity would do on a particle falling a distance d . Likewise to gravity, which has a potential of mgy , the electrical potential above is U e = q 0 Ey When a test charge moves from y 1 to y 2 , the work done on the charge particle by the electric field is: ( 29 ( 29 ) ( 2 1 0 1 0 2 0 1 2 y y E q Ey q Ey q U U U W - = - - = - - = - =

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( 29 ) ( 2 1 0 1 2 y y E q U U U W - = - - = - =
Electric potential For an infinitesimal displacement ds of a charge, the work done by the electric field is F e ·d s = q 0 E ·d s. As this amount of work is done by the electric field, the potential energy of the charge-field system is changed by an amount dU = - q0 E ·d s. The change in potential to move a charge in an electrical field from A to B is then given by: - = B A s d E q U 0

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- = B A s d E q U 0 Because the Electric field is conservative, it does not matter what path connects A and B , the change in potential will be the same. The potential energy per unit charge is U/q 0 . This value is independent of q 0 and has a value at every point in an electric field. U/q 0 is called the electric potential, or simply the potential. The electric potential (a number or scalar not a vector) at any point in the electric field is defined by: 0 q U V =
The potential difference between in two points A and B in an electric field more generally is given by: - = = B A ds E q U V 0 Hence W = qV The unit of a volt is Joules/Coulomb = J/C .

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