// maxwell_eqn.c   computer many of Maxwell's Equations
#include <stdio.h>
#include <stdlib.h>
#include <math.h>

// constants
static double c = 299.792458E+6 ; // speed of light, meters per second, L/T
static double pi = 3.1415926535897932384626433832795028841971 ; // pi, radians
static double eps0 = 8.854E-12; // permittivity vacuum, farads/meter,
                                // units T^2Q^2/ML^3
static double mu0 = 0.0; // pi*4E-7 permeability vacuum, henry/meter,
                         // units ML/Q^2 (eps0*mu0 units T^2/L^2)

// dimensional units
// L length in meters
// T time in seconds
// M mass in kilograms
// Q charge in 

int main(int argc, char *argv[])
{
  double Q; // electric charge in coulombs, units Q, 6.291E+18 electrons
            // charge on one farad capacitor to produce one volt
  double mass; // mass in kilograms, units M
  double T; // time in seconds, units T
  double length; // length in meters, units L
  double speed;  // speed in meters per second, units L/T
  double E[3]; // electric field in volts per meter, units ML/T^2Q
  double D[3]; // electric displacement in coulomb per square meter, units Q/L^2
  double B[3]; // magnetic flux in weber per square meter, units M/TQ
  double H[3]; // magnetic intensity in ampere per meter, Q/TL
  double J; // current density in amperes per square meter, units Q/TL^2
  double I; // current in amperes, coulombs per second, units Q/T
  double V; // voltage in volts, units ML^2/T^2Q ( V=IR )
  double R; // resistance in ohms, units ML^2/TQ^2
  double C; // capacitance in farads, units T^2Q^2/ML^2
            // C = Q/V, parallel plate C = eps0*area/spacing
  double L; // inductance in henrys, units ML^2/Q^2
  double rho; // charge density in coulomb per cubic meter, units Q/L^3
  double lambda; // wave length in meters, units L
  double omega; // angular frequency in radians per second, units 1/T
  double F; // frequency in hertz, cycles per second, units 2*pi/T
  double impedance; // free space 120*pi ohm, units ML^2/TQ^2
                    // capacitor Z = 1/omega*C*i = 1/2*pi*f*c*i , i=sqrt(-1)
                    // inductor  Z = omega*L = 2*pi*F*L
  double energy; // joules, units ML^2/T^2
                 // stored energy = 1/2 CV^2 = 1/2 LI^2
  double power; // watts = joules per second, units ML^2/T^3
                // I^2R, V^2/R, 

  double cchk;
  mu0 = pi*4.0E-7;

  printf("maxwell_eqn.c demonstration running \n");
  printf("values of constants in this program \n");
  printf("c = %e speed of light in meters per second, units L/T \n", c);
  printf("pi = %e radians, no units \n", pi);
  printf("eps0 = %e permittivity vacuum, farads/meter, units T^2Q^2/ML^3 \n", eps0);
  printf("mu0 = %e permeability vacuum, henry/meter, units ML/Q^2 \n", mu0);
  cchk = 1.0/sqrt(eps0*mu0);
  printf("check 1/sqrt(eps0*mu0) = c = %e \n", cchk);
  printf("\n");
  printf("definition and units of variables used in this program \n");
  printf("rho = charge density per unit volume, units Q/L^3 \n");
  printf("E electric field in volts per meter, units ML/T^2Q \n");
  printf("  vector, value in x, y, z direction, may change with time \n");
  printf("D electric displacement in coulomb per square meter, units Q/L^2\n");
  printf("  D = eps0 E \n");
  printf("B magnetic flux in weber per square meter, units M/TQ \n");
  printf("  vector, value in x, y, z direction, may change with time \n");
  printf("H magnetic intensity in ampere per meter, Q/TL \n");
  printf("  H = 1/mu0 B \n");
  printf("J current density in amperes per square meter, units Q/TL^2 \n");
  printf("Q electric charge in coulombs, units Q, 6.291E+18 electrons \n");
  printf("I current in amperes, coulombs per second, units Q/T \n");
  printf("R resistance in ohms, units ML^2/TQ^2 \n");
  printf("V voltage in volts, units ML^2/T^2Q ( V=IR ) \n");
  printf("C capacitance in farads, units T^2Q^2/ML^2 \n");
  printf("  C = Q/V, parallel plate C = eps0*area/spacing \n");
  printf("L inductance in henrys, units ML^2/Q^2 \n");
  printf("lambda wave length in meters, units L \n");
  printf("T time in seconds, units T \n");
  printf("F frequency in hertz, cycles per second, units 2*pi/T \n");
  printf("omega angular frequency in radians per second, units 1/T \n");
  printf(" \n");
  printf(" equations, d is partial derivative \n");
  printf("div E = rho/eps0 \n");
  printf("div B = 0 \n");
  printf("curl E = - dB/dt \n");
  printf("curl B = mu0 * (J + eps0* dE/dt) \n");
  printf("div D = rho \n");
  printf("curl H = J + dD/dt \n");
  printf("V = L dI/dT \n");
  printf("I = C dV/dt \n");

  printf(" \n");
  printf("wave equations \n");
  printf("del^2 E = 1/c^2 d^2E/dt^2 \n");
  printf("del^2 B = 1/c^2 d^2B/dt^2 \n");
  printf(" V = I omega L  single frequency alternating current \n");
  printf(" I = V omega C  complex numbers used to represent phase\n");
  printf(" \n");

  printf("charge Q = integral over volume of rho \n");
  printf("current I = integral over surface of J dot ds \n");

  printf(" \n");
  printf("math definitions dE/dx partial derivative of E with respect to x \n");
  printf("dEz/dy partial derivative of z component of E with respect to y \n");
  printf("divergence, del dot E, div E = dE/dx + dE/dy + dE/dz \n");
  printf("curl, del cross E, curl E = [dEz/dy - dEy/dz, dEx/dz - dEz/dx, \n");
  printf("                             dEy/dx - dEx/dy] vector in x,y,z \n");
  printf("d^2E/dt^2 second derivative of E with respect to t \n");
  printf("del^2 E is Laplacian of E = d^2E/dx^2 + d^2E/dy^2 + d^2E/dz^2 \n");
  printf(" \n");
  printf("Simulation in three dimensions, x,y,z and time t   may use \n");
  printf("a four dimensional array with each element containing: \n");
  printf(" E, B, J, rho, and possibly mass and velocity, etc \n"); 
  printf(" \n");

  printf("maxwell_eqn.c finished \n");
  return 0;
} // end main