# HR24 - 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 discreet 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 tak U W Electric Potential Energy : change in potential energy e it from an initial position to a final position . ( ) Consider an electric charge moving from an initial position at point A to a final position at point B under the i f i i f x f i x o x x U U U W F x dx q = - = - = - nfluence of a known electric field . The force exerted on the charge is: o f f o 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 = - f o i U q E ds = - r r (24 - 2)
A B The change in potential energy of a charge moving under the influence of from point A to point B is: Please note that depends on the valu o f f i o i q E U U U W q E ds U = - = - = - The electric potential V r r r e of o q We define the in such a manner so that is is independent of : Here In all physical problems only changes in are involved. Thus w f o f i f i o o i U W q V V V V V V E ds q q V = = - = - - = - electric potential V r r 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 P with potential The poten f P P P V E d V s V V V = - = = r r tial depends only on the coordinates of P and on P V E r P P V E ds = - r r (24 - 3)

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O Definition of voltage : Units of : J/C known as the "Volt" Consider a pont charge placed at the origin. We will use the defini o W q q V V = - SI Units of Potential due to a point charge V : P 2 2 tion given in the previous page to determine the potential at point P a distnce from O. cos0 The electric field generated by is: 4 4 R P R R o P o V R V E ds Edr Edr q q E r q dr V r πε = - = = = = r r 2 1 1 4 1 4 R P R o o dr R x x q q V r = - = = - 1 4 P o q V R = (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 P is calculated using the principle of super V Potential due to a group of point charges 1 3 1 2 1 2 2 3 3 1 2 1 2 3 1 2 3 1 2 3 position We determine the potentials , and generated by each charge at point P.

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HR24 - Chapter 24 Electric Potential In this chapter we...

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