Search This Blog

Saturday, April 24, 2010

How to do Gauss's law with NON-uniform charge density inside a non-conducting material

The vast majority of Gauss's law problems we do deal with uniform charge densities for non-conductors/insulators. These are the cases where there is charge inside the material, and therefore an electric field, and our job is to find the electric field inside. When the charge density, rho, is constant/uniform, the classic result is the field is linear with r. That is the result whether we have a sphere or a cylinder, and would be the same for gravity, electric fields, or magnetic fields (using Ampere's law).

But what about NON-uniform charge density, where rho depends on radius, r? What do we do with Gauss's law to find the electric fields inside these type of materials and objects? This video is an example of how to handle it. The gist is we need to set up an integral where we add the charges within skinny, hollow spheres of charge. Each little sphere has its own charge density value, and so the charge of each hollow shell is rho x dV. The trick is the dV = (4*pi*r^2)(dr), at least for a sphere. The dr is the small thickness of the hollow shell. The same idea holds for cylinders, where dV = (2*pi*L*r)(dr). I hope this helps!


  1. Great its is really enjoying video, really enjoying ful video, Awesome work, Thanks for share this.

    custom essay

  2. Our pneumatic factory was founded in 2000,CHECK HERE. In decades of serving China pneumatic industry, we have built our reputation on product knowledge, world class suppliers, application support, and value add services. Our commitment to our employees, customers and vendors is the core of our business beliefs. In our factory, there are more than 80 front-line workers, 3000 squares working shop.Our main products are air Pneumatic Cylinder, solenoid valve and also a lot of pneumatic fittings like Air Gun.

  3. Does the process change when the radius we are looking at is outside the non-uniformly charged cylinder?

  4. The capstone project templates are to find the electric fields inside these type of materials and objects.