Electric field due to dipole (Vector)

electric_field

Vector of the electric field. See electric_field_strength.

Symbol:

E

Latex:

\({\vec E}\)

Dimension:

voltage/length

electric_dipole_moment

Vector of the electric_dipole_moment.

Symbol:

p

Latex:

\({\vec p}\)

Dimension:

charge*length

position_vector

Position vector of the point in space. See distance_to_origin.

Symbol:

r

Latex:

\({\vec r}\)

Dimension:

length

electric_field_law

E = (3 * dot(p, r) / norm(r)^5 * r - p / norm(r)^3) / (4 * pi * epsilon_0)

Latex:

\[{\vec E} = \frac{\frac{3 \left( {\vec p}, {\vec r} \right)}{\left \Vert {\vec r} \right \Vert^{5}} {\vec r} - \frac{{\vec p}}{\left \Vert {\vec r} \right \Vert^{3}}}{4 \pi \varepsilon_0}\]

electric_dipole_moment_law

p = 4 * pi * epsilon_0 * (3 * dot(E, r) / 2 * norm(r) * r - norm(r)^3 * E)

Latex:

\[{\vec p} = 4 \pi \varepsilon_0 \left(\frac{3 \left( {\vec E}, {\vec r} \right)}{2} \left \Vert {\vec r} \right \Vert {\vec r} - \left \Vert {\vec r} \right \Vert^{3} {\vec E}\right)\]