Coordinate systems for electric fields.

[Skullmonkee]

Im curious about an electric field (somewhere of radius s) inside a solid sphere (radius a) such that:

$$\int E.da=E4\pi s^{2}$$
and Q = $$\frac{\rho 4\pi s^{3}}{\epsilon_{o}3}$$

What is the difference between using each coordinate system to solve for E? It's just that I've really had to teach my self most maths involved with physics and although i can do most things, sometimes fundamental definitions escape me.
I tried searching for an answer but found it hard to understand the difference between spherical and Cartesian x, y, z coordinates. Am i right in assuming that the above is solved with Cartesian coordinates?
Im sure this is a very stupid and basic question.

 

[marcusl]

The choice of coordinate system can be matched to natural symmetries in the problem. Choosing an "unnatural" system generally makes the equations very difficult, although the resulting solution is still valid. For a spherical system, the natural coordinates are spherical. (Makes sense?) Note that you wrote an equation above in terms of radius s, which is one of the spherical coordinates. Expressing this in cartesian coordinates would be far more complicated since
$$s=\sqrt{x^2 + y^2 + z^2}.$$

To summarize: You are exploiting symmetry in the solution. The flux through a spherical surface surrounding a part of the medium depends only on its radius, so spherical coordinates are the logical and simplest choice in this case.

 

[Skullmonkee]

Thankyou. I'm using the radius rather than a point xyz so its sperical. Makes sense.

Thanks again.