Electric Field Calculation for Volume and Surface Charges?

[timothy ser]

Hello,

I know you can use Gauss' law to calculate the electric field of volume and surface charges but i cannot figure out a way to do it using Coloumb's law. I have several questions about this: when you integrate the charge density in Coloumb's law over the volume is the r^2 inside or outside the integral? is the unit vector necessary to calculate within the integral or is it allowed to drop the unit vector and obtain a scalar equation for the electric field's magnitude? Lastly, when I calculate the electric field of volume charges, i notice that after I integrate, I lose spatial coordinates with which to calculate the electric field at certain points in space.

I am sorry for the long post but I have been struggling with this for sometime.

 

[blue_leaf77]

In Gauss' law the electric field in a certain point in space is a superposition from electric field due to infinitesimal charge element, The E field due to single element is the same as that due to a point charge $k\frac{q}{r^2} \hat{\mathbf{r}}$ - different charge element will have different $r$ and $\hat{\mathbf{r}}$. This means, they are dependent on the variable of integration and hence cannot be taken outside the integral.

Lastly, when I calculate the electric field of volume charges, i notice that after I integrate, I lose spatial coordinates with which to calculate the electric field at certain points in space.

That cannot be true, you should check again your calculation.

 

[timothy ser]

Can somebody due an example with both Gauss' law and Coloumb's law?

 

[jtbell]

Choose an example that you tried to do, preferably one that you already know the answer for, from Gauss's law or otherwise. Write up your attempt at integrating Coulomb's law for it, and post it in the homework section (even though it's not a class assignment). Then people can tell you what you did wrong and give hints on how to proceed.

https://www.physicsforums.com/forums/advanced-physics-homework.154/

 

[timothy ser]

thank you

 

[Drakkith]

Write up your attempt at integrating Coulomb's law for it, and post it in the homework section (even though it's not a class assignment). Then people can tell you what you did wrong and give hints on how to proceed.

Seconded. Thread locked.