feature-kindAvailable
Electric Currents
div((sigma + i*omega*epsilon)*grad(V)) = 0
Reference contract
| Field | Value | Description |
|---|---|---|
| area | AC/DC | — |
| boundaryFeatures | [{"assemblyRole":"essential","displayName":"Voltage Terminal","entityDimensions":["boundary"],"fields":[{"default":"1[V]","name":"magnitude","required":true,"unit":"V","valueType":"expression"},{"default":"0[deg]","name":"phase","required":true,"unit":"deg","valueType":"expression"}],"kind":"Terminal","multiple":true,"parentCategory":"physics","role":"exclusive","targetField":"V"},{"assemblyRole":"essential","displayName":"Electric Potential","entityDimensions":["boundary"],"fields":[{"default":"0[V]","name":"magnitude","required":true,"unit":"V","valueType":"expression"},{"default":"0[deg]","name":"phase","required":true,"unit":"deg","valueType":"expression"}],"kind":"Electric Potential","multiple":true,"parentCategory":"physics","role":"exclusive","targetField":"V"},{"assemblyRole":"essential","displayName":"Ground","entityDimensions":["boundary"],"fields":{},"kind":"Ground","multiple":true,"parentCategory":"physics","role":"exclusive","targetField":"V"},{"assemblyRole":"flux","displayName":"Current Terminal","entityDimensions":["boundary"],"fields":[{"default":"1[A]","name":"current","required":true,"unit":"A","valueType":"expression"},{"default":"0[deg]","name":"phase","required":true,"unit":"deg","valueType":"expression"}],"kind":"Current Terminal","multiple":true,"parentCategory":"physics","role":"contributing","targetField":"V"},{"assemblyRole":"flux","displayName":"Normal Current Density","entityDimensions":["boundary"],"fields":[{"default":"0[A/m^2]","name":"currentDensity","required":true,"unit":"A/m^2","valueType":"expression"},{"default":"0[deg]","name":"phase","required":true,"unit":"deg","valueType":"expression"}],"kind":"Normal Current Density","multiple":true,"parentCategory":"physics","role":"contributing","targetField":"V"},{"assemblyRole":"none","displayName":"Electric Insulation","entityDimensions":["boundary"],"fields":{},"kind":"Electric Insulation","multiple":true,"parentCategory":"physics","role":"contributing","targetField":"V"}] | — |
| childCategories | ["physics.domain","physics.boundary"] | — |
| defaultMaterial | null | — |
| displayName | Electric Currents | — |
| domainFeatures | [{"assemblyRole":"material","displayName":"Conductive Media","entityDimensions":["domain"],"fields":[{"default":"1[S/m]","name":"conductivity","required":true,"unit":"S/m","valueType":"expression"},{"default":"8.8541878188e-12[F/m]","name":"permittivity","required":true,"unit":"F/m","valueType":"expression"}],"kind":"Conductive Media","multiple":true,"parentCategory":"physics","required":true,"targetField":"V"},{"assemblyRole":"volume-source","displayName":"Volume Current Source","entityDimensions":["domain"],"fields":[{"default":"0[A/m^3]","name":"value","required":true,"unit":"A/m^3","valueType":"expression"}],"kind":"Volume Current Source","multiple":true,"parentCategory":"physics","required":false,"targetField":"V"}] | — |
| kind | Electric Currents | — |
| materialSchema | [{"default":"1[S/m]","name":"conductivity","rank":"scalar","required":true,"unit":"S/m"},{"default":"8.8541878188e-12[F/m]","name":"permittivity","rank":"scalar","required":true,"unit":"F/m"}] | — |
| publishedFields | [{"components":1,"displayName":"Electric-potential magnitude","expression":"abs(ec.V)","name":"ec.V","plottable":true,"rank":"scalar","studies":["stationary","frequency-domain"],"unit":"V"},{"components":1,"displayName":"Electric potential, real part","expression":"real(ec.V)","name":"ec.Vreal","plottable":true,"rank":"scalar","studies":["frequency-domain"],"unit":"V"},{"components":1,"displayName":"Electric potential, imaginary part","expression":"imag(ec.V)","name":"ec.Vimag","plottable":true,"rank":"scalar","studies":["frequency-domain"],"unit":"V"},{"components":1,"displayName":"Electric-potential magnitude","expression":"abs(ec.V)","name":"ec.absV","plottable":true,"rank":"scalar","studies":["frequency-domain"],"unit":"V"},{"components":1,"displayName":"Electric-potential phase","expression":"arg(ec.V)","name":"ec.phase","plottable":true,"rank":"scalar","studies":["frequency-domain"],"unit":"rad"},{"components":1,"displayName":"Electric-field magnitude","expression":"norm(-grad(ec.V))","name":"ec.normE","plottable":true,"rank":"scalar","studies":["stationary","frequency-domain"],"unit":"V/m"},{"components":1,"displayName":"Current-density magnitude","expression":"norm(-(conductivity+i*angularFrequency*permittivity)*grad(ec.V))","name":"ec.normJ","plottable":true,"rank":"scalar","studies":["stationary","frequency-domain"],"unit":"A/m^2"},{"components":1,"displayName":"Frequency","expression":"frequency","name":"ec.frequency","plottable":true,"rank":"scalar","studies":["frequency-domain"],"unit":"Hz"},{"components":1,"displayName":"Angular frequency","expression":"angularFrequency","name":"ec.angularFrequency","plottable":true,"rank":"scalar","studies":["frequency-domain"],"unit":"rad/s"}] | — |
| status | certified | — |
| studies | ["Stationary","Frequency Domain"] | — |
| studyCapabilities | [{"certified":true,"differentiability":"exact-ad","kind":"stationary","reason":"september-2026-classroom verified contract: inverse potential scaling with conductivity for a fixed volume-current source"},{"certified":true,"differentiability":"exact-ad","kind":"frequency-domain","reason":"september-2026-classroom verified contract: terminal-current conservation and analytical complex-admittance frequency ratio"}] | — |
| tag | ec | — |
| visible | true | — |
div((sigma + iomegaepsilon)*grad(V)) = 0
Contract
| Property | Value |
|---|---|
| area | AC/DC |
| boundaryFeatures | [{"assemblyRole":"essential","displayName":"Voltage Terminal","entityDimensions":["boundary"],"fields":[{"default":"1[V]","name":"magnitude","required":true,"unit":"V","valueType":"expression"},{"default":"0[deg]","name":"phase","required":true,"unit":"deg","valueType":"expression"}],"kind":"Terminal","multiple":true,"parentCategory":"physics","role":"exclusive","targetField":"V"},{"assemblyRole":"essential","displayName":"Electric Potential","entityDimensions":["boundary"],"fields":[{"defaul... |
| childCategories | ["physics.domain","physics.boundary"] |
| defaultMaterial | null |
| displayName | Electric Currents |
| domainFeatures | [{"assemblyRole":"material","displayName":"Conductive Media","entityDimensions":["domain"],"fields":[{"default":"1[S/m]","name":"conductivity","required":true,"unit":"S/m","valueType":"expression"},{"default":"8.8541878188e-12[F/m]","name":"permittivity","required":true,"unit":"F/m","valueType":"expression"}],"kind":"Conductive Media","multiple":true,"parentCategory":"physics","required":true,"targetField":"V"},{"assemblyRole":"volume-source","displayName":"Volume Current Source","entityDimen... |
| kind | Electric Currents |
| materialSchema | [{"default":"1[S/m]","name":"conductivity","rank":"scalar","required":true,"unit":"S/m"},{"default":"8.8541878188e-12[F/m]","name":"permittivity","rank":"scalar","required":true,"unit":"F/m"}] |
| publishedFields | [{"components":1,"displayName":"Electric-potential magnitude","expression":"abs(ec.V)","name":"ec.V","plottable":true,"rank":"scalar","studies":["stationary","frequency-domain"],"unit":"V"},{"components":1,"displayName":"Electric potential, real part","expression":"real(ec.V)","name":"ec.Vreal","plottable":true,"rank":"scalar","studies":["frequency-domain"],"unit":"V"},{"components":1,"displayName":"Electric potential, imaginary part","expression":"imag(ec.V)","name":"ec.Vimag","plottable":tr... |
| status | certified |
| studies | ["Stationary","Frequency Domain"] |
| studyCapabilities | [{"certified":true,"differentiability":"exact-ad","kind":"stationary","reason":"september-2026-classroom verified contract: inverse potential scaling with conductivity for a fixed volume-current source"},{"certified":true,"differentiability":"exact-ad","kind":"frequency-domain","reason":"september-2026-classroom verified contract: terminal-current conservation and analytical complex-admittance frequency ratio"}] |
| tag | ec |
| visible | true |