MagneticField.js

function MagneticField() {
	this.mmts = []; // magnetic moments in the field

	this.addmmt = function(mx,my,px,py) {
		this.mmts.push({
			m: new p5.Vector(mx,my),	  // the moment vector
			pos: new p5.Vector(px,py) 	// its position in the field
		})
	}

	this.getValue = function(x,y) {
		var v = new p5.Vector(0,0)
		for (var i = 0; i < this.mmts.length; i++) {
			var mm = this.mmts[i]
			var r = new p5.Vector(x,y).sub(mm.pos).mult(0.01),
				rmag = r.mag(),
				v1 = p5.Vector.mult(r, 3 * mm.m.dot(r) / pow(rmag,5))
				v2 = p5.Vector.mult(mm.m, -pow(rmag,-3))
			v.add(p5.Vector.add(v1,v2))
		}
		return v
	}
}

Particle.js

function Particle(x,y, f) {
	this.pos = new p5.Vector(x,y);
	this.inipos = this.pos.copy();
	this.vel = new p5.Vector(0,0);
	this.f = f;
	this.hist = []
	this.dispLength = 0;
	this.dispStart = 0;
	this.done = false

	this.color = color(255);

	this.show = function() {
		pg.stroke(255)

		var startI = int(this.dispStart*this.hist.length),
			endI = startI + int(this.dispLength*this.hist.length)

		pg.beginShape()
		for (var i = startI; i < endI; i++) {
			if(i>=this.hist.length || i<0) continue;
			pg.vertex(this.hist[i].x,this.hist[i].y)
		}
		pg.endShape()
	}

	// integrates field f, 
	// optionally  integrates backward from starting point 
	this.update = function(n,h) {
		var n = n ? n : 1;
		var h = h ? h : 0.01;
		for (var i=0; i<n; i++) { 
			var midVal = p5.Vector.add(
				this.pos,
				p5.Vector.mult(
					this.f.getValue(this.pos.x,this.pos.y),
					h/2)
				)

			this.pos.add(
				p5.Vector.mult(
					this.f.getValue(midVal.x,midVal.y),
					h
					).limit(5)
				)
		}
		this.hist.push(this.pos.copy())
	}

}