What’s left is an integral of the surface element over the surface of the sphere and that’s obviously the surface of the sphere. That means one can take it out of the integral, being a constant. Again due of symmetry considerations E must be the same in any point of the surface of the sphere.
One can now drop the vectors for the scalar product. Ok, here it is, look at the integral form, left term: by symmetry considerations, must be along the radius, but has the same property. One can easily see where the originates from (hopefully you know that the surface of the sphere is ). Where r is the distance from the center of the sphere. The electric field for such a charge is easy to calculate: By adding up the thin shells, one can see that for a sphere of spherically symmetrical distributed charge, the field outside is like the whole charge is in the center of the sphere. One could easily see why it should be zero in the center of the sphere by using symmetry, it requires a little bit more to see why it goes the same in some other points, by noticing that while the field drops with, the surface enclosed by opposing cones is. It’s easy to see that what I said about the gravitational field in the previous post applies to the electric field, too, by the same symmetry considerations: for a thin shell of charge with charge density distributed spherically symmetric, the field outside is as if all the charge is in the center of the sphere, while inside the field is zero. It says that the electric charges are the sources and sinks for the electric field, the electric flux through a closed surface is proportional with the charge inside. is the charge density and is obviously the electric field vector. Where Q is the total charge in the volume V, S is the surface around the volume V. We end up with Gauss law:īy applying Gauss theorem it can be written in integral form: This is electrostatics, so we can drop anything that has a time derivative in there, electric current and obviously, magnetic field. They are also on the header picture of this blog, on the right. A quick look at Maxwell equations shouldn’t hurt, either. The Physicsįor such a simple application, one could start with Coulomb’s law and a simple definition for the potential. This project was also an opportunity for some tests on the methods I implemented. Otherwise the implemented numerical methods (except Euler and perhaps midpoint) are overkill. I implemented Runge-Kutta instead – it includes Euler as a particular case, though – to present more numerical methods and to have something for later, hopefully I’ll reuse the code. The program presented is one of the few cases where the Euler method would be ok, it does not need much precision since it’s only for visualization purposes. Also there is some more multithreading involved. The numerical methods might be a little more difficult, though. The program is simpler because there is no OpenGL. Here is a video of the program in action: Something still simple for now, a program to visualize the electric field in 2D. So here it is, something linked to Maxwell and with his equations.
This means that the field is stronger closer to the object.The first post on this blog dealt with Newtonian mechanics, it seems natural to follow it with another big name in physics and another important field. The closer together the arrows are, the stronger the field and the greater the force experienced by charges in that field.The direction of the arrow shows the way a positive charge will be pushed.įields are usually shown as diagrams with arrows: Electric field shapesĪn electric field is a region where charges experience a force. Since the person, their head, and each of the hair follicles are all positively charged, the hairs will repel from the head and from every other strand causing them to stick out from the head in all directions. The same will happen to each of their hairs.
This force will act on any charged particle in the electric field around the generator.Ī person touching the dome of the Van de Graaff generator will also lose electrons and become positively charged.
A person does not have to touch the Van de Graaff generator to start feeling the effects, as static electricity is a non-contact force. A Van de Graaff generator removes electrons to produce a positive charge.