Section 3.4: Superposition
The principle of superposition states that the net electric force or net electric field on a charge due to multiple other charges is the vector sum of the individual forces or fields produced by each charge independently:
\[ \vec{F}_{\text{net}} = \vec{F}_1 + \vec{F}_2 + \cdots + \vec{F}_n \]
Similarly, for electric fields:
\[ \vec{E}_{\text{net}} = \vec{E}_1 + \vec{E}_2 + \cdots + \vec{E}_n \]
Each contribution is calculated as if the other charges were absent.
Example: Net Force on a Charge
Two charges \(q_1 = 2 \, \mu\text{C}\) and \(q_2 = -3 \, \mu\text{C}\) are placed 0.5 m apart. Find the net force on \(q_1\) if \(q_1\) experiences only the force due to \(q_2\).
\[
F = k \frac{|q_1 q_2|}{r^2} = \frac{(8.99\times10^9)(2\times10^{-6})(3\times10^{-6})}{(0.5)^2} \approx 0.2158\,\text{N}
\]
The direction is attractive toward \(q_2\).
Practice Problems
- Three charges are located at the vertices of a triangle. Compute the net force on one charge.
- Two positive charges of +5 μC and +2 μC are 0.3 m apart. Find the net electric field at the midpoint.
- Explain why the principle of superposition is valid for electric forces.
- Four charges of equal magnitude are placed at the corners of a square. Calculate the net force on one corner charge.
- Derive the net electric field at the center of a line of three equally spaced charges of alternating signs.