Algebra and Calculus in three dimensions

[Avatrin]

Hi

I have realized that I am horrible at setting up integrals in three dimensions when working with Coulomb's law (F = k q*∫r^-2dq ). I don't have the vaguest idea how I can solve this using it and the superposition principle:

An electric charge +Q is distributed with a p(r) which does not depend on θ or ϕ throughout the volume of a sphere of radius R; i.e., it is spherically symmetric. Find the force it produces on an electron (charge -e) located at an outside point r meters from the center of the sphere. Let i point from the origin, at the center of the sphere, to the electron.

I am not asking for a solution to this exercise. I want a good books that can teach me algebra and geometry in three dimensions (a lot of books seem to teach trigonometry in two dimensions and just give you the three dimensional equations without explaining them). If the book also has some multivariable and vector calculus, that will be even better.

 

[UltrafastPED]

Use Gauss' Theorem is the traditional approach ... unless you are very traditional, then you can use Newton's "Shell Theorem" from gravitational theory.

 

[Avatrin]

Like I wrote in my earlier post; I am not looking for a solution to that particular exercise. I just need to become better with geometry and multivariable calculus. I do not have much problem with problems in two dimensions, but setting up integrals in three dimensions dimensions is something I am struggling too much with.

 

[Mmm_Pasta]

The problem you wrote is essentially one-dimensional. Have you taken a course on single-variable calculus? Are you familiar with different coordinate systems? What E&M textbook are you using?

It's hard to recommend something if we do not know what level you are at.

 

[UltrafastPED]

Try "Div, Grad, Curl and all that" by Schey; it is probably the best book of its kind if you will be doing E&M.

https://www.amazon.com/dp/0393925161/?tag=pfamazon01-20

 

[Avatrin]

The problem you wrote is essentially one-dimensional. Have you taken a course on single-variable calculus? Are you familiar with different coordinate systems? What E&M textbook are you using?

It's hard to recommend something if we do not know what level you are at.

Yes, I have taken both single and multivariable calculus (there was too little vector calculus in that course). I have also taken real and complex analysis, abstract algebra and linear algebra.

The thing I am struggling most with happens to be what I need most in physics (I regret I didn't go for programming instead of physics).

My example was obviously a bad one considering it can be solved using Gauss's theorem, but the point was that I struggle with setting up integrals for problems in three dimensions (distances between a point and any point on a sphere and the like). I have no problems solving them when I have set them up.