Voltage is line integral of electric field

In electrostatics, voltage change between two points can be found as the line integral of the electric field along any path connecting the two points.

Conditions:

1. Applies to electrostatic fields, although electrostatic approximation might be used for electromagnetic fields at lower frequencies.

Links:

1. Physics LibreTexts, formula 7.3.18.

voltage

voltage between two points.

Symbol:

V

Latex:

\(V\)

Dimension:

voltage

distance

euclidean_distance traveled.

Symbol:

d

Latex:

\(d\)

Dimension:

length

electric_field_component

Component of the electric field vector tangent to the integration path. See electric_field_strength.

Symbol:

E_s(d)

Latex:

\(E_{s}{\left(d \right)}\)

Dimension:

voltage/length

initial_distance

Initial distance.

Symbol:

s_0

Latex:

\(s_{0}\)

Dimension:

length

final_distance

Final distance.

Symbol:

s_1

Latex:

\(s_{1}\)

Dimension:

length

law

V = -Integral(E_s(d), (d, s_0, s_1))

Latex:

\[V = - \int\limits_{s_{0}}^{s_{1}} E_{s}{\left(d \right)}\, dd\]