<math> \mathbf{q(r)} = -k\nabla T(\mathbf{r}) \quad \leftrightarrow \quad \mathbf{E(r)} = - \nabla \Phi(\mathbf{r})</math>
The table below summarizes the analogous thermal and electrical quantities:
{| class="wikitable"
|-
! scope="col"| Electrostatic Thermal Item! scope="col"| Corresponding Thermal Electrical Item
|-
| style="width:200px;" | Electric Scalar Potential
| style="width:200px;" | Temperature
| style="width:200px;" | Electric Scalar Potential
|-
| style="width:200px;" | Electric Field
| style="width:200px;" | Heat Flux Density
| style="width:200px;" | Electric Field
|-
| style="width:200px;" | Perfect Electric Conductor
| style="width:200px;" | Perfect Thermal Conductor
| style="width:200px;" | Perfect Electric Conductor
|-
| style="width:200px;" | Dielectric Material
| style="width:200px;" | Insulator Material
| style="width:200px;" | Dielectric Material
|-
| style="width:200px;" | Volume Charge
| style="width:200px;" | Volume Heat Source
| style="width:200px;" | Volume Charge
|}