If you possess the necessary mathematical knowledge to calculate points, you have the ability to utilize a spline in order to visually represent magnetic lines. Here is an example of how this can be achieved:
// Utilize your mathematical calculations to create an array of THREE.Vector3 points
var points = [ v1, v2, v3, v4, and so on ];
var curve = new THREE.SplineCurve3( points );
var geometry = new THREE.Geometry();
// Adjust the segment count to influence the smoothness of the line.
geometry.vertices = curve.getPoints( 50 );
var material = new THREE.LineBasicMaterial( { color : 0xff0000 } );
// Construct the final Object3d to incorporate into the scene
var splineObject = new THREE.Line( geometry, material );
This information is sourced directly from the documentation and can be accessed here
You may also find MathBox intriguing, as mentioned in this answer here.