=== Defining Field Integrals ===
It is often needed to compute integrals of the electric or magnetic fields to define other related quantities. The following table shows some of widely used field integralsin electrostatics and magnetostatics. In EM.Ferma, you can define a path integral along a line segment that is parallel to one of the three principal axes, or a loop integral on a rectangle that is parallel to one of the principal planes. You can also define flux planes or flux boxes. All this is done from the same Field Integral Dialog. To define a Field Integral, right-click on "Field Integrals" in the Navigation Tree and select "Insert New Observable..." from the contextual menu. The Integral Type drop-down list gives nine options as listed in the table below:
{| class="wikitable"
|-
! scope="col"| Quantity
! scope="col"| Field Integral
! scope="col"| Definition
! scope="col"| Output Data File
|-
! scope="row"| Voltage
| <math> V = \int_C \mathbf{E(r)} . \mathbf{dl} </math>
| voltage.DAT
|-
! scope="row"| Current
| <math> I = \oint_{C_o} \mathbf{H(r)} . \mathbf{dl} </math>
| current.DAT
|-
! scope="row"| Electric Flux
| <math> \Phi_E = \int\int_{S_o} \mathbf{D(r)} . \mathbf{ds} = \int\int_{S_o} \epsilon \mathbf{E(r)} . \mathbf{ds} </math>
| flux_E.DAT
|-
! scope="row"| Magnetic Flux
| <math> \Phi_H = \int\int_S \mathbf{B(r)} . \mathbf{ds} = \int\int_S \mu \mathbf{H(r)} . \mathbf{ds} </math>
| flux_H.DAT
|-
! scope="row"| Electric Energy
| <math> W_E = \int \int \int_V \epsilon \vert \mathbf{E(r)} \vert ^2 dv </math>
| energy_E.DAT
|-
! scope="row"| Magnetic Energy
| <math> W_H = \int\int\int_V \mu \vert \mathbf{H(r)} \vert ^2 dv </math>
| energy_H.DAT
|-
! scope="row"| Capacitance
| <math> C = Q/V = \int\int_{S_o} \epsilon \mathbf{E(r)} . \mathbf{ds} / \int_C \mathbf{E(r)} . \mathbf{dl} </math>
| capacitance.DAT
|-
! scope="row"| Inductance
| <math> L = \Phi_H/I = \int\int_S \mu \mathbf{H(r)} . \mathbf{ds} / \oint_{C_o} \mathbf{H(r)} . \mathbf{dl} </math>
| inductance.DAT
|-
! scope="row"| Resistance
| <math> R = V/I_{cond} = \int_C \mathbf{E(r)} . \mathbf{dl} / \int\int_S \mathbf{J(r)} . \mathbf{ds} = \int_C \mathbf{E(r)} . \mathbf{dl} / \int\int_S \sigma \mathbf{E(r)} . \mathbf{ds} </math>
| resistance.DAT
|}
In the above table, C represents an open curve (path), C<sub>o</sub> represents a closed curve (loop), S represents an open surface like a plane, S<sub>o</sub> represents a closed surface like a box, and V represents a volume. In EM.Ferma, you can define a path integral along a line segment that is parallel to one of the three principal axes, or a loop integral on a rectangle that is parallel to one of the principal planes. You can also define flux planes or flux boxes. All this is done from the same Field Integral Dialog. To define a Field Integral, right-click on "Field Integrals" in the Navigation Tree and select "Insert New Observable..." from the contextual menu. The Integral Type drop-down list gives five options: {| class="wikitable"|-! scope="col"| Field Integral Type! scope="col"| Output Data File(s)|-! scope="row"| Voltage Path| voltage.DAT|-! scope="row"| Current Loop| current.DAT|-! scope="row"| Flux Plane| flux_H.DAT|-! scope="row"| Flux Box| flux_E.DAT|-! scope="row"| Energy Box| energy_E.DAT & energy_H.DAT|} The domain of the field integral is set using the "Integration Box Coordinates" section of the Field Integral dialog. Box domains are specified by the coordinates of two opposite corners. Voltage Path requires a line; therefore, two of the coordinates of the two corners must be identical. Otherwise, an error message will pop up. For example, (0, 0, 0) for Corner 1 and (10, 0, 0) for Corner 2 define a Z-directed line segment. Current Loop requires a rectangle; therefore, one of the coordinates of the two corners must be identical. For example, (0, 0, 0) for Corner 1 and (10, 10, 0) for Corner 2 define a rectangle in the XY plane.
After the completion of a static simulation, the result of the field integrals are written into ".DAT" data files. These files can be accessed using [[EM.Cube]]'s Data Manager.
{{Note| If you define a single Flux Box observable and a single Voltage Path observable for your static project, the Capacitance is calculated and written to "capacitance.DAT" data file.}}
{{Note| If you define a single Flux Plane observable and a single Current Loop observable for your static project, the Inductance is calculated and written to "inductance .DAT" data file.}}
== Modeling Transmission Lines Using EM.Ferma==