Voltage and Electric Potential

Flashcards covering key vocabulary and concepts related to voltage and electric potential from the lecture notes.

Electric Potential

An important scalar quantity associated with electrostatic fields, represented by V, where E = -∇V. It is measured in volts and E always points towards decreasing values of V.

Conservative Vector Field

An electrostatic E-field is described as such because its curl is zero (∇ × E = 0) and the line integral of E over any closed path is zero (∮ E·dl = 0).

Electric Potential Function (V)

A scalar function whose negative gradient represents the E-field (E = -∇V). It is also known as the electrostatic potential function or scalar potential function, measured in volts.

Voltage (Vab)

Defined as the negative line integral of the E-field between two points Pa and Pb (Vab = -∫(from Pb to Pa) E·dl). For electrostatic fields, it also equals the difference of electric potentials at the endpoints (Vab = Va - Vb).

Potential Difference

A term interchangeable with 'voltage' for electrostatic fields, signifying that the voltage between two points is independent of the path of integration chosen between them.

Work per Unit Charge

The voltage Vab between two points represents the amount of work per unit charge done by the electric field when a positive test charge is moved from Pa to Pb along a given path.

Voltage Sign Convention

By convention, for Vab, a '+' sign is located at the first point (Pa) and a '-' sign at the second point (Pb), and 'V' can denote the voltage difference between these points.

Electric Potential of a Point Charge

The potential V at a radial distance R from a point charge Q, referenced to infinity, given by the formula V = Q / (4πεR).

Electric Potential for Multiple Point Charges

The total potential V generated by a collection of N point charges is the sum of individual potentials: V = (1 / 4πε) Σ(from k=1 to N) (Qk / |r - rk'|).

Electric Potential for Volume-Charge Distribution

The potential V generated by a volume charge distribution ρv is given by the integral V = (1 / 4πε) ∫_Vol (ρv dv' / |r - r'|).

Electric Potential for Surface-Charge Distribution

The potential V generated by a surface charge distribution ρs is given by the integral V = (1 / 4πε) ∫_S (ρs ds' / |r - r'|).

Electric Potential for Line-Charge Distribution

The potential V generated by a line charge distribution ρl is given by the integral V = (1 / 4πε) ∫_C (ρl dl' / |r - r'|).