Electric potential is a scalar-field view of the electric field. We analyze electrical phenomena from the viewpoints of work and energy.
Basic Knowledge
Electric potential V [V = J/C]: The work required to bring a unit positive charge from infinity.
Electric potential at a point a distance r from point charge Q: V = kQ/r
Relationship between electric field E and potential V (uniform electric field): E = −ΔV/Δx (the electric field is the slope of the potential)
Electric potential energy of charge q:U = qV
Equipotential surface: A surface connecting points with equal potential. It is always perpendicular to the electric field (electric field lines).
No work is done when a charge is moved along an equipotential surface.
The potential difference (voltage) between two points is V_AB = V_A − V_B, and the work done by the electric field when charge q moves from A to B is:W = q(V_A − V_B) = qV_AB
Electric potential V (electric potential) (Potential energy per unit charge. Unit: V = J/C)
Potential difference and voltage (The difference in potential between two points. V_AB = V_A − V_B)
Equipotential surface (A surface consisting of points at the same potential. Perpendicular to the electric field)
Potential energy U (U = qV. The positional energy of a charge)
Relationship between electric field and potential (E = −dV/dx. The electric field is the negative gradient of potential)
Further Study (Background and Significance)
Because potential is a scalar quantity, superposition requires only algebraic addition. The potential produced by multiple point charges is V = Σ(kQᵢ/rᵢ) (a signed sum). It is easier to calculate than the electric field, so in entrance examinations it is effective to calculate the electric field from the potential.
A conductor in electrostatic equilibrium becomes an equipotential body, and its surface becomes an equipotential surface. The electric field inside is zero (electrostatic shielding). This is the principle of shielding in electronic equipment.
The electron volt (eV) is an energy unit used in atomic and nuclear physics: 1 eV = 1.6 × 10⁻¹⁹ J.
- Electric potential V = kQ/r (scalar, with sign)
- With potential difference V_AB, work W = qV_AB
- Equipotential surfaces and electric fields are perpendicular
- Superposition of potential: algebraic sum
- E = −dV/dx (the slope of potential is the electric field)
- A conductor is an equipotential body (inside, E = 0)
- 1 eV = 1.6 × 10⁻¹⁹ J
Points to Note (Easily Confused)
① Potential is a scalar, while the electric field is a vector. ② Zero potential and zero electric field are independent conditions. ③ The sign of W = qV_AB: if q is positive and V_A > V_B, then W > 0 (the electric field does positive work). ④ A negative charge is forced toward the higher potential (opposite to the direction of the electric field).
Practice
- Find the potential at a point 0.30 m from a point charge +3.0 × 10⁻⁶ C (k = 9.0 × 10⁹).
- When charge 2.0 × 10⁻³ C moves between two points with a potential difference of 100 V, find the work done by the electric field.
- State the relationship between equipotential surfaces and electric field lines.