Potential Due to a Group of Charges

# Potential Due to a Group of Charges - Physics 202 Tuesday...

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Physics 202 Tuesday, February 16, 1999 Announcements: None Lecture notes: Potential Due to a Group of Charges V = V 1 + V 2 V = ( Q1/ 4 πε o r1) + ( Q2/ 4 πε o r2) o the result is a scalar quantity Similarly, V = Σ V i = Σ (Q i / 4 πε o r i ) What is the change in potential energy if we bring a charge q from point

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A to point B in the presence of point charge Q? o U = U B - U A = q(V B - V A ) = q [ Q/4 πε o ][ (1/r B ) - (1/r A )] Consider the case when r A = infinity, then using the above expression it is natural to choose U A = 0 for as the potential approaches infinity. o U B = q [ Q/4 πε o ] (1/r B ) o Thus, in general .... U(r) = q [ Q/4 πε o r] Therefore, the potential energy of the system of charges, q and Q, at a distance of r from each other is equal to the change in potential energy when we bring then from infinitely far apart to a separation of r. o work is done by external forces If work is done by electrostatic forces on a charge ( or charges) then U = - W due to electrostatic force .
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