Electric potential
Section: Electric Fields | Syllabus: Cambridge A Level Physics (9702)
Electric Potential (V)
Electric potential at a point is the work done per unit positive charge in bringing a small test charge from infinity to that point. It is a scalar quantity.
V = (Q/4π_0 r)The unit is the Volt (V), where 1 V = 1 J C^-1. Potential is positive near +Q and negative near -Q.
Equipotential Surfaces
An equipotential surface is a surface where the electric potential is the same at all points. No work is done when a charge moves along an equipotential surface (W = qΔ V, and Δ V = 0).
- Point Charge: Equipotentials are concentric spheres.
- Uniform Field: Equipotentials are equally spaced parallel planes.
- Rule: Equipotential lines always meet electric field lines at 90^.
Electric Potential Energy (E_P)
The electric potential energy of two point charges (Q and q) separated by r is:
E_P = (Qq/4π_0 r)Worked Examples
Worked Example 1: Net PotentialQuestion: How far from a -5.0 nC charge, along the line connecting it to a +8.0 nC charge (40 mm away), is the electric potential zero?
Solution1. Let the point be x from -5.0 nC. The distance from +8.0 nC is (40 - x).
2. V_total = V_1 + V_2 = 0 k(-5.0 × 10^-9)x + k(8.0 × 10^-9)40 - x = 0.
3. (5/x) = (8/40-x) 200 - 5x = 8x 13x = 200 x = 15.4 mm.
Worked Example 2: Potential DifferenceQuestion: Find the P.D. between points X (6.0 cm from 10 nC) and Y (10.0 cm from 10 nC).
Solution1. V_x = kQ / r_x = (8.99 × 10^9 × 10 × 10^-9) / 0.06 = 1498 V.
2. V_y = kQ / r_y = (8.99 × 10^9 × 10 × 10^-9) / 0.10 = 899 V.
3. Δ V = 1498 - 899 = 599 V (or ≈ 600 V).
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