Understanding Electric Potential, Energy, and Fields

Electric Potential

Electric potential represents the potential energy of a unit positive charge located in an electric field. The electrical potential difference between point A and point B equals the work done by the electric field in moving the unit positive charge from A to B: (V_a - V_b = ∫ E · dr). The electric potential at a point in space is the work done by the electric field to move a unit positive charge from that point to infinity. Its SI unit is the Volt.

If a positive charge q is moved from A to B, the work done by the electric field is: W = q (V_a - V_b). The electric potential energy of a charge at a point in space is related to the electric potential at that point by: E_p = q · V

Potential Energy of a System of Charges

E_p = K (Q₁ · Q₂/R₁₂ + Q₁ · Q₃/R₁₃ + Q₂ · Q₃/R₂₃)

Field Lines

Field lines are drawn to meet the following conditions:

• At every point in space, the electric field vector is tangent to the field lines and has the same direction as the field lines.

Equipotential Surfaces

Equipotential surfaces are obtained by joining points in space that are at the same electric potential. They have the following properties:

• They are perpendicular to the field lines at any point.
• The work done by the electric field to move a charge from one point to another on the same equipotential surface is zero. Proof: W = q (V_a - V_b) = 0, since V_a = V_b, therefore work = 0.

Analogies Between Gravitational and Electric Fields

• Both fields are created by a point mass or charge, so both are central. Their field lines are open and have radial symmetry.
• Both fields are conservative, so they have an associated potential energy (E_p) and potential. The work done against the field is stored as E_p and can be fully recovered.
• The field intensity is directly proportional to the mass or charge that creates it and inversely proportional to the square of the distance between the mass or charge and the point where we calculate the field.

Differences: Electric Field

• Electric forces can be attractive or repulsive. Field lines always originate on positive charges and terminate on negative charges.
• The constant K depends on the medium in which it operates. In a vacuum, K = 9 x 10⁹.

Differences: Gravitational Field

• Gravitational forces are always attractive. The field lines point towards the mass that creates it.
• The constant G is universal and does not depend on the medium in which it acts. G = 6.67 x 10^-11.