Divergence of electric displacement field is volumetric charge density¶

The divergence of the electric induction field (also known as the electric displacement field) is equal to the volumetric charge density at all points in space. Another form of this law states that there exist electric charges.

Links:

position_vector¶: Position vector of a point in space. See distance_to_origin.

Symbol:: r
Latex:: \({\vec r}\)
Dimension:: length

electric_displacement¶: Vector field of the electric_displacement as a function of the position_vector.

Symbol:: D(r)
Latex:: \({\vec D} \left( {\vec r} \right)\)
Dimension:: charge/area

volumetric_charge_density¶: Scalar field of the volumetric_charge_density as a function of the position_vector.

Symbol:: rho(r)
Latex:: \(\rho{\left({\vec r} \right)}\)
Dimension:: charge/volume

law¶

div(D(r)) = rho(r)

Latex:: \[\text{div} \, {\vec D} \left( {\vec r} \right) = \rho{\left({\vec r} \right)}\]