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import { COULOMB_CONSTANT, electricField, type Charge, type Point } from './electricField';
export const VACUUM_PERMITTIVITY = 8.8541878128e-12;
export const ELEMENTARY_CHARGE = 1.602176634e-19;
const THERMAL_ENERGY_EV = 8.617333262e-5 * 300;
function positive(...values: number[]) {
if (values.some(value => !Number.isFinite(value) || value <= 0)) {
throw new RangeError('Physical dimensions and material constants must be finite and positive.');
}
}
/** Vacuum potential in volts, referenced to infinity. Undefined inside the
* same 0.18 m visualization exclusion used by electricField. */
export function potential(point: Point, charges: readonly Charge[]): number {
let volts = 0;
for (const charge of charges) {
if (charge.coulombs === 0) continue;
const r = Math.hypot(point.x - charge.x, point.y - charge.y, point.z - charge.z);
if (r < 0.18) return NaN;
volts += COULOMB_CONSTANT * charge.coulombs / r;
}
return volts;
}
/** Force on a test charge, excluding that charge from the supplied sources. */
export function forceOn(test: Charge, sources: readonly Charge[]): Point {
const field = electricField(test, sources);
return { x: field.x * test.coulombs, y: field.y * test.coulombs, z: field.z * test.coulombs };
}
export function pairEnergy(q1: number, q2: number, separation: number): number {
positive(separation);
return COULOMB_CONSTANT * q1 * q2 / separation;
}
/** Exact signed flux for an origin-centred spherical Gaussian surface.
* A point charge exactly on the surface makes the integral undefined. */
export function gaussianFlux(charges: readonly Charge[], radius: number): number {
positive(radius);
let enclosed = 0;
for (const charge of charges) {
if (charge.coulombs === 0) continue;
const r = Math.hypot(charge.x, charge.y, charge.z);
if (Math.abs(r - radius) < 1e-9) return NaN;
if (r < radius) enclosed += charge.coulombs;
}
return enclosed / VACUUM_PERMITTIVITY;
}
export interface CapacitorParameters {
area: number;
gap: number;
relativePermittivity: number;
voltage: number;
/** If isolated, voltage means the initial vacuum charging voltage. */
isolated?: boolean;
}
export function capacitor(p: CapacitorParameters) {
positive(p.area, p.gap, p.relativePermittivity);
const vacuumCapacitance = VACUUM_PERMITTIVITY * p.area / p.gap;
const capacitance = vacuumCapacitance * p.relativePermittivity;
const voltage = p.isolated ? p.voltage / p.relativePermittivity : p.voltage;
const charge = capacitance * voltage;
const field = voltage / p.gap;
return {
capacitance, voltage, charge, field,
energy: 0.5 * capacitance * voltage ** 2,
polarization: VACUUM_PERMITTIVITY * (p.relativePermittivity - 1) * field,
};
}
export interface ConductorParameters {
voltage: number;
resistivity: number;
length: number;
area: number;
carrierDensity: number;
}
export function conductor(p: ConductorParameters) {
positive(p.resistivity, p.length, p.area, p.carrierDensity);
const resistance = p.resistivity * p.length / p.area;
const current = p.voltage / resistance;
return {
resistance, current,
power: p.voltage * current,
density: current / p.area,
electronDrift: -current / (p.carrierDensity * ELEMENTARY_CHARGE * p.area),
};
}
export interface SemiconductorParameters {
intrinsicDensity: number;
/** Fully ionized donors minus acceptors, in m^-3. */
netDoping: number;
electronMobility: number;
holeMobility: number;
}
/** Non-degenerate thermal equilibrium at 300 K. Solving for the minority
* through mass action avoids catastrophic subtraction at large doping. */
export function semiconductor(p: SemiconductorParameters) {
positive(p.intrinsicDensity, p.electronMobility, p.holeMobility);
const majority = (Math.abs(p.netDoping) + Math.hypot(p.netDoping, 2 * p.intrinsicDensity)) / 2;
const minority = p.intrinsicDensity ** 2 / majority;
const electrons = p.netDoping >= 0 ? majority : minority;
const holes = p.netDoping >= 0 ? minority : majority;
return {
electrons, holes,
fermiShift: THERMAL_ENERGY_EV * Math.log(electrons / p.intrinsicDensity),
conductivity: ELEMENTARY_CHARGE * (electrons * p.electronMobility + holes * p.holeMobility),
};
}
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