Section 3.8: Work by Electric Forces
The electric force is conservative, which means the work done in moving a charge between two points depends only on the potential difference between those points, not on the path taken.
\[ W = -\Delta U = q \Delta V \]
where \( W \) is the work done by the electric force, \( \Delta U \) is the change in potential energy, \( q \) is the charge, and \( \Delta V \) is the potential difference.
Example 1
A proton moves from a point at potential \( V_1 = 120 \, \text{V} \) to \( V_2 = 40 \, \text{V} \). Find the work done by the electric force.
\[ \Delta V = V_2 - V_1 = 40 - 120 = -80 \, \text{V} \]
\[ W = q \Delta V = (1.6 \times 10^{-19} \, C)(-80 \, V) = -1.28 \times 10^{-17} \, J \]
The negative sign indicates the force did negative work (the proton moved to a lower potential).
Practice Problems
- What is the work done to move a -2 μC charge through a potential difference of +12 V?
- Explain why electric forces are conservative.
- A charge moves in a closed path in an electric field. What is the total work done?
- Calculate the change in potential energy of an electron moving through a 200 V potential difference.
- Conceptual: How is the concept of work by electric forces connected to energy conservation?