Set 51 Problem number 12

Problem

Point A is at potential 38 volts and point B is at potential 12 Volts.  How much work is required to move a charge of -2.203 C from a point A to point B?

Solution

The potential difference from the initial point to the final is 12 Volts - 38 Volts = -26.02 Volts. The work is the product of the charge and the potential difference: (-2.203 C)(-26.02 Volts) = (-2.203 C)(-26.02 J/C) = 57.3 J.

Generalized Solution

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. 

Explanation in terms of Figure(s), Extension

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.
• This can be understood as follows:  (`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). 

Figure(s)