Problem: A charge of 79 C moves from a point at potential 1 volts to a point at potential 90 Volts. How much work must be done to accomplish this?
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Solution: The potential difference from the initial point to the final is 90 Volts - 1 Volts = 89 Volts. The work is the product of the charge and the potential difference: ( 79 C)( 89 Volts) = ( 79 C)( 89 J/C) = 7031 J.
Generalized Response: When a charge Q moves from a point at potential V1 to a point at potential V2, it passes through a potential difference `dV = V2 - V1. The potential difference is measured in volts = Joules / Coulomb; the charge is measured in Coulombs. Moving a positive charge through a positive potential difference is analogous to raising a mass against the force of gravity, which requires positive work. So the work done to get the charge through the potential difference is W = Q `dV.
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Figure description: The figure below shows a charge Q moving from a low potential V1 to a high potential V2. The potential difference is `dV = V2 - V1, and the work required to move the charge is W = Q `dV (`dV is measured in Joules of work required per Coulomb of charge, so work must be the product of Q (Coulombs) and `dV (Joules / Coulomb) ).
