Question

This is not for an assignment, but for my own understanding and I was wondering if anyone would be able to assist me with understanding.

Consider a non-trivial trajectory where the velocity & acceleration of some charged particle are non-zero.

If i were wanting to plot the electric and magnetic field, how would I go about making the equation to do so? Would you be able to give me an example?

If I wanted to convert a 2 dimensional plot to 3 dimensions, would I only need to add another direction to do so?

For example, consider an equation making a particle moving radially outward into a spiralling shape in 2 dimensions. Could I add an increasing variable in the Z direction to make the spiral into a cone shape?

Or perhaps even a more simple suggestion, If I have a particle circling at a constant radius on origin, would adding an increasing variable in the Z direction cause that circle to become spring?

I would love to see an example of an equation showing one or both of these concepts. I also wish to plot your equations on a software like Maple or Mathematica to get a visual representation.

Answer 1