lecture06

# Fundamentals of Physics, (Chapters 21- 44) (Volume 2)

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Chapter 24 Electric Potential In this chapter we will define the electric potential ( symbol V ) associated with the electric force and accomplish the following tasks: Calculate V if we know the corresponding electric field. Calculate the electric field if we know the corresponding potential V. Determine the potential V generated by a point charge. Determine the potential V generated by a discrete charge distribution. Determine the potential V generated by a continuous charge distribution. Determine the electric potential energy U of a system of charges. Define the notion of an equipotential surface. Explore the geometric relationship between equipotential surfaces and electric field lines. Explore the potential of a charged isolated conductor. (24-1)

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A B O x . . . x i x x f F ( x ) In Chapter 8 we defined the associated with a conservative force as the negative value of the work that the force must do on a particle to take U W ! Electric Potential Energy change in potential energy 0 it from an initial position to a final position . ( ) Consider an electric charge moving from an initial position at point to a final position at point under the inf f i i f x f i x x x U U U W F x dx q A B ! = " = " = " # 0 0 luence of a known electric field . The force exerted on the charge is . f f i i E F q E U F ds q E ds = ! = " \$ = " \$ # # r r r r r r r ( ) f i x x U F x dx ! = " # 0 f i U q E ds ! = " # \$ r r (24-2)
A B 0 0 The change in potential energy of a charge moving under the influence of from point A to point is: . Please note that depends on the val f f i i q E B U U U W q E ds U ! = " = " = " # ! \$ The Electric Potential r r r V 0 ue of . q 0 0 0 We define the in such a manner so that it is independent of : Here . In all physical problems only changes in are involved. Thus w f f i f i i U W q V V V V V V E ds q q V ! ! = = " ! = " # " = " \$ % electric potential r r V e can define arbitrarily the value of at a reference point, which we choose to be at infinity: 0. We take the initial position as the generic point with potential : The pote . f P P P V V V P V s V E d = = = " \$ % r r ntial depends only on the coordinates of and on . P V P E r P P V E ds ! = " # \$ r r (24-3)

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0 Definition of voltage : Units of : Consider a point charge placed at the origin. We J/C wi , known as the volt ll use the defini W q V q V ! = " Potential Due to a Point Ch SI Units of : a e rg V P 2 0 2 0 tion given on the previous page to determine the potential at point a distance from . cos0 The electric field generated by is: 4 4 R P R R P V P R O V E ds Edr Edr q q E r q dr V r #\$ % % % = " = = = = r r 2 0 0 1 1 4 1 4 R P R dr q q V r x x R % % ( ) * = " = + , - " . = !" = (24-4)
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lecture06 - Chapter 24 Electric Potential In this chapter...

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