# Coulomb triple integral for a sphere

• Luke Bower
In summary: If you're getting a different answer, you might need to try differentiating the equation more.Differentiating could give you a better idea of what's going on.Differentiating could give you a better idea of what's going on.
Luke Bower

## Homework Statement

Find the electric field of a sphere of radius R and charge Q outside sphere. Use only a Coulomb integral to do this.

## Homework Equations

I know that I have to use a triple integral to find the E-field. I am just unsure of my whole setup really.

## The Attempt at a Solution

I tried setting up a triple integral of (0-2pi),(0,R) and then I don't know what to put for the the bounds of the third.

You need to assume some more information. Is the charge distribution spherically symmetric?
In spherical coordinates, your three coordinates are ##(r,\theta,\phi)##. Do you know what the valid range is for the ##\theta## coordinate? If not, you'd better study up on the spherical coordinate system.

Luke Bower said:

## Homework Statement

Find the electric field of a sphere of radius R and charge Q outside sphere. Use only a Coulomb integral to do this.

## Homework Equations

I know that I have to use a triple integral to find the E-field. I am just unsure of my whole setup really.

## The Attempt at a Solution

I tried setting up a triple integral of (0-2pi),(0,R) and then I don't know what to put for the the bounds of the third.
Could you please provide the actual problem statement? Your version is kind of ambiguous.

Problem statement: find th electric field of a sphere of radius R and charge Q outside the sphere. Do this using BOTH a gauss's law and coulomb integral.

I have done the gaussian one, which was pretty easy. I just can't figure out the coulomb integral.

No i have not used spherical coordinates before and it is not a prereq for this course apparently. But if i have to do it then i have to ha

I appreciate any help.

Is that the problem statement as given to you word for word? It still seems kind of vague. Charge Q outside the sphere? Q could be anywhere then, except on or inside the sphere. Do you mean Q is on the surface of the sphere? If so, is it distributed uniformly? Is the sphere conducting or is it an insulator?

vela said:
Is that the problem statement as given to you word for word? It still seems kind of vague. Charge Q outside the sphere? Q could be anywhere then, except on or inside the sphere. Do you mean Q is on the surface of the sphere? If so, is it distributed uniformly? Is the sphere conducting or is it an insulator?

My teacher said the sphere is conducting. And yes that is word for word. He is very vague in all of his problem statements.

Wow TCC Engineering Physics II I'm guessing.

If it's a conducting sphere, the charge is going to distributed on the surface, so you only have to integrate over the surface.

You've probably worked out or seen worked out the electric field due to a ring of charge. Try using that result by splitting up the sphere into a bunch of infinitesimal rings.

jugglar456 said:
Wow TCC Engineering Physics II I'm guessing.

jugglar456 said:
Wow TCC Engineering Physics II I'm guessing.
yeah pretty much ha

vela said:
If it's a conducting sphere, the charge is going to distributed on the surface, so you only have to integrate over the surface.

You've probably worked out or seen worked out the electric field due to a ring of charge. Try using that result by splitting up the sphere into a bunch of infinitesimal rings.
Ok so it would only be a double integral and not a triple integral right? because it would just be the area and the volume would not be taken into account.

Right. You're integrating over an area, a two-dimensional surface, so it would be a double integral.

well i asked my teacher today and he said that would have to assume a non-conducting sphere, (was told by classmate that he said conducting ha). So he suggested the same thing as you to find the E-field due to a coin shape of charge. Which I have, and then assume the sphere is composed of infitesimal rings like that

When I work it out I end up getting a different answer than my gaussian surface. Its close but only off by 1/(4R)

## 1. What is a Coulomb triple integral for a sphere?

A Coulomb triple integral for a sphere is a mathematical concept used to calculate the electric field due to a spherical charge distribution. It takes into account the distance from the center of the sphere to any point in space and the charge density at that point.

## 2. How is the Coulomb triple integral for a sphere different from other types of integrals?

The Coulomb triple integral for a sphere differs from other types of integrals because it takes into account the three-dimensional nature of the charge distribution. It also requires the use of spherical coordinates instead of the traditional Cartesian coordinates.

## 3. What is the formula for the Coulomb triple integral for a sphere?

The formula for the Coulomb triple integral for a sphere is given by ∭(ρ/4πε0) (r²sinθ) dr dθ dφ, where ρ is the charge density, ε0 is the permittivity of free space, r is the distance from the center of the sphere, and θ and φ are the spherical coordinates.

## 4. How is the Coulomb triple integral for a sphere used in practical applications?

The Coulomb triple integral for a sphere is commonly used in physics and engineering to calculate the electric field at a specific point due to a charged sphere. It is also used in the analysis of electric potential and capacitance of spherical systems.

## 5. What are the limitations of the Coulomb triple integral for a sphere?

The Coulomb triple integral for a sphere assumes that the charge distribution is continuous and spherically symmetric. It also does not take into account the effects of external electric fields or the presence of other nearby charges. Additionally, it may become more complex and difficult to solve for non-uniform charge distributions.

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