//champ electrique dans un point quelconque
#include <iostream>
#include <cmath>

using namespace std;

void fieldComp(double x, double y, double z, 
               double xp, double yp, double zp,
               double q, double &ex, double &ey, double &ez);  
double distanceToPoint(double x, double y, double z, 
                       double xp, double yp, double zp);

//constante dielectrique
const double eps0=8.854e-12;

int main() {
  double R;
  cout << "Entrez le rayon de l'anneau (en m) : ";
  cout << "R = ";   cin >> R;
  double Q;
  cout << "Entrez le charge de l'anneau (en C) : ";
  cout << "Q = ";   cin >> Q;
  int div;
  cout << "Entrez le nombre N de divisions de l'anneau : ";
  cin >> div;
  
  double xp, yp, zp;
  cout << "Entrez les coordonnees du point X (en m) : " << endl;
  cout << "x = ";   cin >> xp;
  cout << "y = ";   cin >> yp;
  cout << "z = ";   cin >> zp;

  /* On imagine l'anneau dans le plan xy, unidimensionnel
    1) l'anneau est divise en N segments
    2) on "boucle" sur les segments de l'anneau
    3) on calcule le champ genere par chaque segment 
    4) on additionne les contributions au champ total. */
  double deltaPhi = 2.*M_PI/div;
  //charge du segment (q et Q sont 2 variables differentes !) 
  double q = Q/div; 

  double xseg, yseg, zseg;
  double phi;
  double distance=0.;
  double ex, ey, ez;
  double fieldX=0., fieldY=0., fieldZ=0.;
  //boucle sur l'anneau
  for (int iseg=0; iseg<div; iseg++) {
    phi = deltaPhi/2. + iseg*deltaPhi;
    xseg = R*cos(phi);
    yseg = R*sin(phi);
    zseg = 0.;
            
    //calcul des composantes du vecteur E
    fieldComp(xseg,yseg,zseg,xp,yp,zp,q,ex,ey,ez);
    
    //et on addition le champ genere par chaque segment
    fieldX += ex;
    fieldY += ey;
    fieldZ += ez;
  }
  
  double fieldXYZ = sqrt(pow(fieldX,2)+pow(fieldY,2)+pow(fieldZ,2));     
  cout << "Estimation du champ: |E| = " << fieldXYZ << " V/m" << endl;
  cout << " Ex = " << fieldX << " V/m" << endl;
  cout << " Ey = " << fieldY << " V/m" << endl;
  cout << " Ez = " << fieldZ << " V/m" << endl;

  return 0;
}

//calcul du champ electrique en X
void fieldComp(double x, double y, double z,
               double xp, double yp, double zp, 
               double q, double &ex, double &ey, double &ez) {

  //calcul de la distance entre le centre du segment et le point X
  double dist = distanceToPoint(x,y,z,xp,yp,zp);

  //champ electrique |E| en X
  double e = 1./(4.*M_PI*eps0) * q / (dist*dist);
     
  //composantes de E
  ex = e * (xp-x) / dist;
  ey = e * (yp-y) / dist;
  ez = e * (zp-z) / dist;
}

//distance entre deux points
double distanceToPoint(double x1, double y1, double z1, 
                       double x2, double y2, double z2) {
  double distance;
  double diffx = x2-x1;
  double diffy = y2-y1;
  double diffz = z2-z1;
  distance = sqrt(pow(diffx,2) + pow(diffy,2) + pow(diffz,2));

  return distance;
}