Section 1.8: Systems of Multiple Charges
This section covers computing net forces and fields when multiple point charges are present using the principle of superposition.
Superposition Principle:
The net force on a charge is the vector sum of forces from all other charges:
\( \vec{F}_{\text{net}} = \sum_i \vec{F}_i = \sum_i k_e \frac{q q_i}{r_i^2} \hat{r}_i \)
Similarly, the net electric field: \( \vec{E}_{\text{net}} = \sum_i \vec{E}_i \)
Example 1
Three charges \( q_1, q_2, q_3 \) are positioned in a line. Compute the net force on \( q_1 \).
\( \vec{F}_1 = \vec{F}_{12} + \vec{F}_{13} \)
Compute each pairwise force using Coulomb's law, then sum vectors taking directions into account.
Practice Problems
- Square configuration of four equal charges; compute net force on one corner.
- Triangular arrangement; calculate net force and field at center.
- Compute net field along axis of linear three-charge system.
- Four charges in a rectangle; determine net electric field at one vertex.
- Superposition of point and line charge: compute net force on a test charge.