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 Δ 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 ff ii if xx fie x t e x t E Ee x t E n e t o U U U W F x dx F x dx Fq E F F F a q Δ= = = = == = = ∫∫ 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 ext E o E E UF d s F d sq E d = = = G GG G f i s G () f i x E x x d x f o i Uq E d s G G (24 - 2) 0 ext E FF += O . . . x i x x f F ext F E x
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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 fie x t E o i o q UU U W W qE d s Uq Δ= = = = Δ The electric potential V G G work done by an external agent ext E WW 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 of i f i oo o i W UW qV V V V V V E d s qq q V Δ Δ = = − → changes G G 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 VV V VE d s == arbitrarily G G he potential depends only on the coordinates of P and on P G P P d s G G (24 - 3) ext Wq V E V =− Δ
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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 VV q q V Δ= 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 RR o P o VR V E ds Edr Edr q q E r qd r V r πε ∞∞ =− = = = = ∫∫ G G 2 1 11 44 R P R oo dr R xx qq V r ⎡⎤ →= = = ⎢⎥ ⎣⎦ 1 4 P o q V R = (24 - 4)
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Alessandro Conte Volta 1745-1827
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Luigi Galvani 1737-1798
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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 generated by this group at any
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This document was uploaded on 11/04/2011 for the course PHY 108 at SUNY Buffalo.

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

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