# ch24 - Chapter 24 Electric Potential In this chapter we...

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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 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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O 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 πε πε = - = = = = r r 2 0 0 1 1 4 1 4 R P R dr q q V r x x R πε πε ? = - = ? - = 0 1 4 P q V R πε = (24-4)
P q 2 Consider the group of three point charges shown in the figure. The potential generated by this group at any point is calculated using the principle of super V P Potential Due to a Group of Point Charges 1 2 3 3 1 2 1 2 3 0 1 1 2 0 1 0 2 0 0 2 0 3 1 2 3 position.

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