Electric Potential Energy

🔖 Topics

Calculate the electric potential energy between two point charges in different orientations
Use conservation of energy to calculation the speed of point charges as they evolve in time

Potential energy is defined as: \(\Delta U = -W_{field}\)
Work is defined as: \(W = \vec{F} \cdot \vec{x}\) for a constant force acting along a straight line path
Definition of electric potential energy for a point charge: \(U = \frac{kQq}{r}\)
- Note that \(U \rightarrow 0\) as \(r \rightarrow \infty\)
- Why do we like to work with energy? Energy is a scalar, not a vector!
- Example: Calculate the electric potential energy a distance away from a point charge.
- Example: Calculate the electric potential energy a distance away from two point charges.
We didn’t do too much with gravitational potential energy in PHY 121, but \(U = - \frac{GMm}{r}\)
We can use conservation of energy, just like in PHY 121 (see practice problems below)

N/A

A positive charge (Q = +5.0 \(\mu C\)) is fixed in place at the origin. Another positive charge (q = +1.0 \(\mu C\) and m = 2.0 kg) is free to move and starts at rest at the point (1.0 m, 0.0 m). What is the speed of q when it is at the point (5.0 m, 0.0 m)? What about when it is infinitely far away from Q?
How much work does it take to place three point charges at the corners of an equilateral triangle that has a side length of 1.0 cm? Two of the charges are +2.0 \(\mu C\) while the last one is -2.0 \(\mu C\).
Suppose I fix a point charge Q = 1.0 mC at the origin of a coordinate system. I place another point charge q = 3.0 mC at the point (1.0 m, 0.0 m) and allow it to move in space. Where could I move this point charge such that no work is done on it? Sketch a diagram of the result.

Giambattista, Alan, et al. College Physics With an Integrated Approach to Forces and Kinematics. 5th ed., McGraw-Hill Education, 2020.