The signs of q and Q determine whether the electric potential energy is positive or negative. For more than two charges, the electric potential energy is the scalar sum of the individual potential energies for each pair of charges.
The electric potential V at a point is the electric potential energy per unit charge when a point charge q is present, assuming U = 0 when q is not present:
Electric potential, like electric potential energy, is a scalar quantity. Potential has a unique value at each point in space. The SI unit for potential is the volt (1 V = 1 J/C).
If a point charge q moves through a potential difference ΔV, then the change in electric potential energy is
ΔUE = qΔV
(17-7)
The electric potential at a distance r from a point charge Q is
The potential at a point P due to N point charges is the sum of the potentials due to each charge.
An equipotential surface has the same potential at every point on the surface. An equipotential surface is perpendicular to the electric field at all points. No change in electric potential energy occurs when a charge moves from one position to another on an equipotential surface. If equipotential surfaces are drawn such that the potential difference between adjacent surfaces is constant, then the surfaces are closer together where the field is stronger.
The electric field always points in the direction of maximum potential decrease.
The potential difference that occurs when you move a distance d in the direction of a uniform electric field of magnitude E is
ΔV = -Ed
(17-10)
The electric field has units of
N/C = V/m.
(17-11)
In electrostatic equilibrium, every point in a conductor must be at the same potential.
A capacitor consists of two conductors (the plates) that are given opposite charges. A capacitor stores charge and electric potential energy. Capacitance is the ratio of the magnitude of charge on each plate (Q) to the electric potential difference between the plates (ΔV). Capacitance is measured in farads (F).
where A is the area of the plates, d is their separation, and ε0 is the permittivity of free space [ε0 = 1/(4πk) = 8.854 × 10-12 C2/(N·m2)]. If vacuum separates the plates, κ = 1; otherwise κ > 1 is the dielectric constant of the dielectric (the insulating material). If a dielectric is immersed in an external electric field, the dielectric constant is the ratio of the external electric field E0 to the electric field E in the dielectric.
