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# 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. The tasks for this chapter are: 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 In chapter 8 we defined the associated with a conservative force as the the work that an external force must do on a particle to take the part U W Electric Potential Energy : change in potential energy icle from an initial position to a final position . ( ) ( ) where and ( 0, 0 ) Consider an electric charge moving from an i f f i i i f x x f i ext ext E x x E ext E net o x x U U U W F x dx F x dx F qE F F F a q = - = = = - = = - = = nitial position at point A to a final position at point B under the influence of a known electric field . The force exerted on the charge is: o f f ext E o i i E F q E U F ds F ds q E d = = × = - × = - × r r r r r r r r f i s r ( ) f i x E x U F x dx = - f o i U q E ds = - × r r (24 - 2) 0 ext E F F + = r r O . . . x i x x f F ext F E x
A B The change in potential energy of a charge moving from point A to point B is: Please note that depends on the value of Note: The o f f i ext E o i o q U U U W W q E ds U q = - = = - = - × The electric potential V r r work done by an external agent ext E W W U = - = ∆ We define the in such a manner so that is is independent of : Here In all physical problems only in are involved f ext E o f i f i o o o i W U W q V V V V V V E ds q q q V = = - = = - - = - × changes r r electric potential V . Thus we can define 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 T P f P P V V V V V E ds = - × = = arbitrarily r r he potential depends only on the coordinates of P and on P V E r P P V E ds = - × r r (24 - 3) ext W q V = E W q V = - ∆

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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 defin " E o W V V q q V = - SI Units of : Potential due to a point charge P 2 2 ition 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 πε = - × = = = = r r 2 1 1 1 4 4 R P R o o dr R x x q q V r πε πε = - = = - 1 4 P o q V R πε = (24 - 4)
Alessandro Conte Volta 1745-1827

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Luigi Galvani 1737-1798
r 1 r 2 r 3 P q 1 q 3 q 2 Consider the group of three point charges shown in the figure. The potential

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