Section 3.7: Superposition of Potentials
The principle of superposition states that the total electric potential due to multiple point charges is the algebraic sum of the potentials due to each charge individually.
\[ V_{total} = \sum_i V_i = \sum_i \frac{1}{4\pi \epsilon_0} \frac{q_i}{r_i} \]
where \( q_i \) is the i-th charge, and \( r_i \) is the distance from that charge to the point of interest.
Example 1
Find the potential at a point P due to two point charges, \( q_1 = 2\,\mu C \) at (0,0,0) and \( q_2 = -3\,\mu C \) at (0,0,2 m).
Compute distances from P to each charge: \( r_1 \) and \( r_2 \).
Calculate individual potentials: \[ V_1 = \frac{1}{4\pi \epsilon_0} \frac{q_1}{r_1}, \quad V_2 = \frac{1}{4\pi \epsilon_0} \frac{q_2}{r_2} \]
Total potential: \( V_{total} = V_1 + V_2 \).
Practice Problems
- Compute the potential at the midpoint of a line connecting two charges +Q and -Q.
- For three charges at vertices of an equilateral triangle, find the potential at the center.
- Explain why potential is scalar while electric field is vector.
- Determine potential at a point along the axis of a linear charge distribution using superposition.
- Conceptual: How does superposition simplify calculation of electric potential?