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Charge.html
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<html>
<style>
.electron {
width: 20px;
height: 20px;
position: absolute;
background-color: green;
border-radius: 50%;
left: 200px;
top: 200px;
}
</style>
<body style="background-color:black;">
<div style="border:2px solid;border-color:white;width:800px;height:600px">
<p>
<button onclick="start()">Start</button>
</p>
<a id="time" style="color:white;"></a>
<div id="electron1" class="electron"></div>
<div id="electron2" class="electron"></div>
</div>
<script>
function make_vector(x_in, y_in, z_in) {
let vector = {
x: x_in,
y: y_in,
z: z_in,
sm: function (scalar) {
return make_vector(scalar * this.x, scalar * this.y, scalar * this.z);
},
add: function (v2) {
return make_vector(this.x + v2.x, this.y + v2.y, this.z + v2.z);
},
sub: function (v2) {
return make_vector(this.x - v2.x, this.y - v2.y, this.z - v2.z);
},
mag: function () {
return Math.sqrt(Math.pow(this.x, 2) + Math.pow(this.y, 2) + Math.pow(this.z, 2));
},
cp: function(v2) {
return make_vector(this.y*v2.z-v2.y*this.z,this.z*v2.x-v2.z*this.x, this.x*v2.y-v2.x*this.y);
}
}
return vector;
}
// Definition of a electron
function make_electron(charge_name) {
// Charge of electron
let q = -1.0;
// Mass of electron
let m = 0.1;
// Initial Position
let x0 = Math.random() * 800.0;
let y0 = Math.random() * 600.0;
let r0 = make_vector(x0, y0, 0);
// Initial velocity of electron
let vx0 = (Math.random() - 0.5) * 10.0;
let vy0 = (Math.random() - 0.5) * 10.0;
let v0 = make_vector(vx0, vy0, 0);
// Define charge object
let charge = {
name: charge_name,
q: q,
m: m,
r: r0,
v: v0,
};
// Returns electron object
return charge;
}
function start() {
// HTML electron
let electron1 = document.getElementById("electron1");
let electron2 = document.getElementById("electron2");
// Define background EField
let efield = make_vector(0.0, 0.0, 0);
let bfield = make_vector(0, 0, 1);
// Make an electron
let e1 = make_electron("electron1");
let e2 = make_electron("electron2");
// Time
let t = 0.0;
let dt = 0.01;
// Timer (ms)
let id1 = setInterval(function () { frame(e1) }, 10);
let id2 = setInterval(function () { frame(e2) }, 10);
// Draw frame
function frame(e) {
// Update time
t = t + dt;
// Force F=qE
let fe = electric_force(efield, e);
let fb = magnetic_force(bfield, e);
// Update acceleration
let a = (fe.add(fb)).sm(1.0/e.m).sm(5.0/e.v.mag());
// Update velocity
let v_old = e.v;
e.v = e.v.add(a.sm(dt));
// Update position
e.r = e.r.add( e.v.sm(0.5*dt).add(v_old.sm(0.5*dt)) );
// Boundary Conditions (Reflecting)
if ((e.r.x < 0) || (e.r.x > 800)) e.v.x = -e.v.x;
if ((e.r.y < 0) || (e.r.y > 800)) e.v.y = -e.v.y;
// Move the HTML object
if (e.name == "electron1") {
electron1.style.left = Math.round(e.r.x) + 'px';
electron1.style.top = Math.round(e.r.y) + 'px';
} else if (e.name == "electron2") {
electron2.style.left = Math.round(e.r.x) + 'px';
electron2.style.top = Math.round(e.r.y) + 'px';
}
console.log('V: ' + e.v.mag() + ' R: ' + e.r.mag());
// Update time
document.getElementById("time").innerHTML = "Time: " + Math.round(t);
}
// Electric Force (F=qE)
function electric_force(efield, charge) {
let f_e = efield.sm(charge.q);
return f_e;
}
// Magnetic Force
function magnetic_force(bfield, charge) {
let vxb = charge.v.cp(bfield);
let f_b = vxb.sm(charge.q);
return f_b;
}
// Coloumb Force
function coulomb(q1, q2, r) {
let k = 4000.0;
let f_e = k * q1 * q2 / Math.pow(r, 2);
return f_e;
}
}
</script>
</body>
</html>