Electromagnetism operators
40 operators in the electromagnetism category of the live registry. Each is a named formula you can compose inside a state contract or call directly through POST /api/zeq/compute. KO42 is always on; add up to three more per call (total ≤ 4), per the 7-step protocol.
| Operator | Description | Equation |
|---|---|---|
EM1 | Lorentz force law giving the total electromagnetic force on a charged particle in electric and magnetic fields. | \vec{F} = q(\vec{E} + \vec{v} \times \vec{B}) |
EM10 | Faraday's law in integral form: EMF equals the negative rate of change of magnetic flux. | \mathcal{E} = -\frac{d\Phi_B}{dt} |
EM11 | Energy stored in a capacitor expressed in terms of capacitance and voltage or charge. | U = \frac{1}{2}CV^2 = \frac{1}{2}\frac{Q^2}{C} |
EM12 | Energy stored in an inductor: one-half times inductance times current squared. | U = \frac{1}{2}LI^2 |
EM13 | Impedance of an RLC circuit combining resistance and net reactance. | Z = \sqrt{R^2 + (X_L - X_C)^2} |
EM14 | AC power delivered to a circuit accounting for the power factor. | P = IV\cos\phi |
EM15 | Poynting vector giving the directional energy flux of an electromagnetic field. | \vec{S} = \frac{1}{\mu_0}\vec{E} \times \vec{B} |
EM2 | Gauss's law: electric flux through a closed surface equals enclosed charge divided by permittivity. | \nabla \cdot \vec{E} = \frac{\rho}{\epsilon_0} |
EM3 | Gauss's law for magnetism: magnetic monopoles do not exist, so magnetic flux through any closed surface is zero. | \nabla \cdot \vec{B} = 0 |
EM4 | Faraday's law of induction: a changing magnetic field generates a curling electric field. | \nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t} |
EM5 | Ampère-Maxwell law: magnetic field curls around currents and changing electric fields. | \nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0\epsilon_0\frac{\partial \vec{E}}{\partial t} |
EM6 | Coulomb electric potential: voltage from a point charge at distance r. | V = \frac{1}{4\pi\epsilon_0}\frac{q}{r} |
EM7 | Electric field as the negative gradient of the electric potential. | \vec{E} = -\nabla V |
EM8 | Magnetic field from a long straight current-carrying wire (Biot-Savart law result). | \vec{B} = \frac{\mu_0 I}{2\pi r}\hat{\phi} |
EM9 | Magnetic flux through a surface as the integral of the magnetic field over that surface. | \Phi_B = \int \vec{B} \cdot d\vec{A} |
EMH1 | Magnetic field intensity H derived from magnetic flux density B in free space. (Renamed from HF1 in A1.2: the HF id namespace is the canonical Truth-Verification/forensic layer — Phase 13.2.) | H_{field}^{(1)} = \frac{B}{\mu_0} |
EMH10 | H-field operator variant 10 for eddy current analysis. (Renamed from HF10 in A1.2: the HF id namespace is the canonical Truth-Verification/forensic layer — Phase 13.2.) | H_{field}^{(10)} = \frac{B}{\mu_0} |
EMH11 | H-field operator variant 11 for skin depth computation. (Renamed from HF11 in A1.2: the HF id namespace is the canonical Truth-Verification/forensic layer — Phase 13.2.) | H_{field}^{(11)} = \frac{B}{\mu_0} |
EMH12 | H-field operator variant 12 for magnetic shielding effectiveness. (Renamed from HF12 in A1.2: the HF id namespace is the canonical Truth-Verification/forensic layer — Phase 13.2.) | H_{field}^{(12)} = \frac{B}{\mu_0} |
EMH13 | H-field operator variant 13 for solenoid field uniformity. (Renamed from HF13 in A1.2: the HF id namespace is the canonical Truth-Verification/forensic layer — Phase 13.2.) | H_{field}^{(13)} = \frac{B}{\mu_0} |
EMH14 | H-field operator variant 14 for toroidal inductor design. (Renamed from HF14 in A1.2: the HF id namespace is the canonical Truth-Verification/forensic layer — Phase 13.2.) | H_{field}^{(14)} = \frac{B}{\mu_0} |
EMH15 | H-field operator variant 15 for transformer core analysis. (Renamed from HF15 in A1.2: the HF id namespace is the canonical Truth-Verification/forensic layer — Phase 13.2.) | H_{field}^{(15)} = \frac{B}{\mu_0} |
EMH16 | H-field operator variant 16 for magnetic recording head design. (Renamed from HF16 in A1.2: the HF id namespace is the canonical Truth-Verification/forensic layer — Phase 13.2.) | H_{field}^{(16)} = \frac{B}{\mu_0} |
EMH17 | H-field operator variant 17 for MRI gradient coil optimization. (Renamed from HF17 in A1.2: the HF id namespace is the canonical Truth-Verification/forensic layer — Phase 13.2.) | H_{field}^{(17)} = \frac{B}{\mu_0} |
EMH18 | H-field operator variant 18 for superconducting magnet design. (Renamed from HF18 in A1.2: the HF id namespace is the canonical Truth-Verification/forensic layer — Phase 13.2.) | H_{field}^{(18)} = \frac{B}{\mu_0} |
EMH19 | H-field operator variant 19 for magnetic levitation force computation. (Renamed from HF19 in A1.2: the HF id namespace is the canonical Truth-Verification/forensic layer — Phase 13.2.) | H_{field}^{(19)} = \frac{B}{\mu_0} |
EMH2 | H-field operator variant 2 for magnetic field intensity computation. (Renamed from HF2 in A1.2: the HF id namespace is the canonical Truth-Verification/forensic layer — Phase 13.2.) | H_{field}^{(2)} = \frac{B}{\mu_0} |
EMH20 | H-field operator variant 20 for electromagnetic compatibility analysis. (Renamed from HF20 in A1.2: the HF id namespace is the canonical Truth-Verification/forensic layer — Phase 13.2.) | H_{field}^{(20)} = \frac{B}{\mu_0} |
EMH21 | H-field operator variant 21 for near-field antenna coupling. (Renamed from HF21 in A1.2: the HF id namespace is the canonical Truth-Verification/forensic layer — Phase 13.2.) | H_{field}^{(21)} = \frac{B}{\mu_0} |
EMH3 | H-field operator variant 3 for paramagnetic material response. (Renamed from HF3 in A1.2: the HF id namespace is the canonical Truth-Verification/forensic layer — Phase 13.2.) | H_{field}^{(3)} = \frac{B}{\mu_0} |
EMH4 | H-field operator variant 4 for diamagnetic material response. (Renamed from HF4 in A1.2: the HF id namespace is the canonical Truth-Verification/forensic layer — Phase 13.2.) | H_{field}^{(4)} = \frac{B}{\mu_0} |
EMH5 | H-field operator variant 5 for ferromagnetic domain analysis. (Renamed from HF5 in A1.2: the HF id namespace is the canonical Truth-Verification/forensic layer — Phase 13.2.) | H_{field}^{(5)} = \frac{B}{\mu_0} |
EMH6 | H-field operator variant 6 for antiferromagnetic ordering. (Renamed from HF6 in A1.2: the HF id namespace is the canonical Truth-Verification/forensic layer — Phase 13.2.) | H_{field}^{(6)} = \frac{B}{\mu_0} |
EMH7 | H-field operator variant 7 for magnetic hysteresis modeling. (Renamed from HF7 in A1.2: the HF id namespace is the canonical Truth-Verification/forensic layer — Phase 13.2.) | H_{field}^{(7)} = \frac{B}{\mu_0} |
EMH8 | H-field operator variant 8 for magnetic anisotropy effects. (Renamed from HF8 in A1.2: the HF id namespace is the canonical Truth-Verification/forensic layer — Phase 13.2.) | H_{field}^{(8)} = \frac{B}{\mu_0} |
EMH9 | H-field operator variant 9 for magnetostrictive coupling. (Renamed from HF9 in A1.2: the HF id namespace is the canonical Truth-Verification/forensic layer — Phase 13.2.) | H_{field}^{(9)} = \frac{B}{\mu_0} |
EO5 | Total electromagnetic field energy density integrated over a volume. | E_5 = \int_V \frac{1}{2}\epsilon_0|\vec{E}|^2 + \frac{1}{2\mu_0}|\vec{B}|^2 dV |
PFC0 | Magnetic flux through a surface as the surface integral of the B field. | -log p(o) + D_KL[q(s)||p(s|o)] |
RF9 | Frequency-dependent voltage divider transfer function for RF circuit analysis. | R_9(\omega) = \frac{V_{out}}{V_{in}} = \frac{Z_2}{Z_1 + Z_2} |
VD | Shockley diode equation relating current to voltage across a p-n junction. | V_D = I_0(e^{qV/k_BT} - 1) |
Compute with one of these
curl -sS -X POST https://zeqsdk.com/api/zeq/compute \
-H "Authorization: Bearer $ZEQ_KEY" \
-H "Content-Type: application/json" \
-d '{"operators":["EM1"],"inputs":{}}'
The response carries the bare physics value, its unit and uncertainty, the generated master equation, and a signed envelope you can verify on any node.
See also
- The solvers — how an operator becomes a physical answer
- Operator selection — how a query picks operators
- All categories — the full reference index