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Electromagnetism operators

40 operators in the electromagnetism category of the live registry. Compose them in a contract or call POST /api/zeq/compute — KO42 is always on, plus up to three more per call.

How it computes: dedicated closed-form solver solveEM — real equations over CODATA-2018 constants; where an operator needs a series/matrix/field a scalar cannot express, it refuses honestly. See the solvers.

OperatorDescriptionEquation
EM1Lorentz 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})
EM10Faraday's law in integral form: EMF equals the negative rate of change of magnetic flux.\mathcal{E} = -\frac{d\Phi_B}{dt}
EM11Energy 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}
EM12Energy stored in an inductor: one-half times inductance times current squared.U = \frac{1}{2}LI^2
EM13Impedance of an RLC circuit combining resistance and net reactance.Z = \sqrt{R^2 + (X_L - X_C)^2}
EM14AC power delivered to a circuit accounting for the power factor.P = IV\cos\phi
EM15Poynting vector giving the directional energy flux of an electromagnetic field.\vec{S} = \frac{1}{\mu_0}\vec{E} \times \vec{B}
EM2Gauss's law: electric flux through a closed surface equals enclosed charge divided by permittivity.\nabla \cdot \vec{E} = \frac{\rho}{\epsilon_0}
EM3Gauss's law for magnetism: magnetic monopoles do not exist, so magnetic flux through any closed surface is zero.\nabla \cdot \vec{B} = 0
EM4Faraday's law of induction: a changing magnetic field generates a curling electric field.\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}
EM5Ampère-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}
EM6Coulomb electric potential: voltage from a point charge at distance r.V = \frac{1}{4\pi\epsilon_0}\frac{q}{r}
EM7Electric field as the negative gradient of the electric potential.\vec{E} = -\nabla V
EM8Magnetic field from a long straight current-carrying wire (Biot-Savart law result).\vec{B} = \frac{\mu_0 I}{2\pi r}\hat{\phi}
EM9Magnetic flux through a surface as the integral of the magnetic field over that surface.\Phi_B = \int \vec{B} \cdot d\vec{A}
EMH1Magnetic field intensity H derived from magnetic flux density B in free space.H_{field}^{(1)} = \frac{B}{\mu_0}
EMH10H-field operator variant 10 for eddy current analysis.H_{field}^{(10)} = \frac{B}{\mu_0}
EMH11H-field operator variant 11 for skin depth computation.H_{field}^{(11)} = \frac{B}{\mu_0}
EMH12H-field operator variant 12 for magnetic shielding effectiveness.H_{field}^{(12)} = \frac{B}{\mu_0}
EMH13H-field operator variant 13 for solenoid field uniformity.H_{field}^{(13)} = \frac{B}{\mu_0}
EMH14H-field operator variant 14 for toroidal inductor design.H_{field}^{(14)} = \frac{B}{\mu_0}
EMH15H-field operator variant 15 for transformer core analysis.H_{field}^{(15)} = \frac{B}{\mu_0}
EMH16H-field operator variant 16 for magnetic recording head design.H_{field}^{(16)} = \frac{B}{\mu_0}
EMH17H-field operator variant 17 for MRI gradient coil optimization.H_{field}^{(17)} = \frac{B}{\mu_0}
EMH18H-field operator variant 18 for superconducting magnet design.H_{field}^{(18)} = \frac{B}{\mu_0}
EMH19H-field operator variant 19 for magnetic levitation force computation.H_{field}^{(19)} = \frac{B}{\mu_0}
EMH2H-field operator variant 2 for magnetic field intensity computation.H_{field}^{(2)} = \frac{B}{\mu_0}
EMH20H-field operator variant 20 for electromagnetic compatibility analysis.H_{field}^{(20)} = \frac{B}{\mu_0}
EMH21H-field operator variant 21 for near-field antenna coupling.H_{field}^{(21)} = \frac{B}{\mu_0}
EMH3H-field operator variant 3 for paramagnetic material response.H_{field}^{(3)} = \frac{B}{\mu_0}
EMH4H-field operator variant 4 for diamagnetic material response.H_{field}^{(4)} = \frac{B}{\mu_0}
EMH5H-field operator variant 5 for ferromagnetic domain analysis.H_{field}^{(5)} = \frac{B}{\mu_0}
EMH6H-field operator variant 6 for antiferromagnetic ordering.H_{field}^{(6)} = \frac{B}{\mu_0}
EMH7H-field operator variant 7 for magnetic hysteresis modeling.H_{field}^{(7)} = \frac{B}{\mu_0}
EMH8H-field operator variant 8 for magnetic anisotropy effects.H_{field}^{(8)} = \frac{B}{\mu_0}
EMH9H-field operator variant 9 for magnetostrictive coupling.H_{field}^{(9)} = \frac{B}{\mu_0}
EO5Total 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
PFC0Magnetic flux through a surface as the surface integral of the B field.-log p(o) + D_KL[q(s)||p(s|o)]
RF9Frequency-dependent voltage divider transfer function for RF circuit analysis.R_9(\omega) = \frac{V_{out}}{V_{in}} = \frac{Z_2}{Z_1 + Z_2}
VDShockley diode equation relating current to voltage across a p-n junction.V_D = I_0(e^{qV/k_BT} - 1)

Compute one — a real call​

Ask the operator which inputs it needs (the honesty contract refuses empty inputs rather than inventing them):

curl -sS -X POST https://zeqsdk.com/api/zeq/operator-spec \
  -H "Content-Type: application/json" \
  -d '{"operator":"EM1"}'

See also​