Electric Field of Dipole, straight line, ring, disk, shell, and sold sphere

[Dottywine]

Homework Statement

Okay, I totally do not understand how to derive the electric field made by a dipole or a line or a ring or etc.

Homework Equations

When finding the electric field, when you make an estimate, saying that the test charge is very far away, it should be similar to kQ/r^2

You may need to know lambda, the linear charge distribution and the ones for area and volume.

The Attempt at a Solution

I've made lots of attempts. Its 2 am right now, but I will upload it tomorrow if anyone needs it. Someone asked a question like this before, if that helps, but I didn't understand the answer and I need help with all of these things.

 

[Defennder]

You have to be more specific if we are to help. But in general, you should make use of this:

$$dE = \frac{dq}{4\pi \varepsilon r(x,y,z)^2}$$. But you probably already knew that. r(x,y,z) is just the distance from the point at which you want you find the E-field to the differential charged element dq in terms of x,y,z coordinates. dq is either lambda dL, rho dV where lambda and rho are the charge densities of the charged object.

And I don't think you need to make any assumption about the test charge being very far away. There are a number of such problems in this forum recently. Do a search of this and you'll find some of them.