Section 3.2: Potential of Point Charges
The electric potential at a point due to a single point charge is the work done per unit charge in bringing a positive test charge from infinity to that point.
Formula:
\[ V = \frac{1}{4\pi\epsilon_0} \frac{q}{r} \]
where \( q \) is the source charge, \( r \) is the distance from the charge to the point, and \( \epsilon_0 \) is the permittivity of free space.
Superposition Principle:
If multiple point charges are present:
\[ V_\text{total} = \sum_i \frac{1}{4\pi\epsilon_0} \frac{q_i}{r_i} \]
The potentials simply add algebraically (scalar addition).
Example 1
Calculate the electric potential at a point 0.3 m from a point charge of 5 μC in vacuum.
\[ V = \frac{1}{4\pi\epsilon_0} \frac{5 \times 10^{-6}}{0.3} \approx 1.5 \times 10^5 \text{ V} \]
Practice Problems
- Compute the potential at the midpoint between two equal charges of 3 μC separated by 0.4 m.
- Find the potential at a point 0.2 m from a -2 μC charge.
- Explain why electric potential is a scalar while electric field is a vector.
- Calculate the potential due to three point charges arranged in a triangle.
- For two charges +q and -q separated by distance d, find the potential at the midpoint.