# Total Charge what? potential by line inter

• Phymath
In summary, the conversation discusses finding the total charge and potential associated with a given equation. The first part involves calculating the charge density and using it to find the total charge by integrating over a specific volume. The limit for the integral is determined by the symmetry of the charge distribution. The second part involves using line integration to find the potential difference between two points.
Phymath
alright, so i got this potentional equation $$\Phi = k_e Q e^{-\alpha r}/r$$
it askes me to find the total charge after calcing the charge density, so
anyway...lets get the field $$\vec{E}=-\nabla \Phi$$
so yea then take the divergence fot the charge density
$$\nabla \bullet \vec{E} = 4 \pi k_e p$$
so then I am assuming to figure out the "total charge" I am going to use the density in a volume intergral and equate that to $$4 \pi k_e Q_{enclosed}$$ but what is my limit? is it is a sphere i can define by radius a as my surface? or what?

next question

finding the potential associated with a Vector field A by line intergration in polar cords (or any cords for that matter) what's that mean
$$\oint \vec{A} \bullet d\vec{r} = \Phi (b) - \Phi (a)$$ is that what they're talking about let me know

I can't exactly follow what you are talking about in the first case. Perpaps you could state the problem more specifically. The potential certainly suggests a spherically symmetric charge distribution. Is that potential good for all r?

Your second question is more or less right, but that integration symbol is for closed path integrals where the resulting potential difference would be zero. You want an integral from point a to point b.

alright arlight,

the first one the total charge is what I am asking what is the "total charge" mean

$$\int \int^{2\pi}_0 \int^{\pi}_0 \nabla \bullet (-\nabla \Phi) dV = 4 \pi k_e Q_e$$
whats the last limits to solve for $$Q_e$$

Have you calculated divE yet? That gives you the charge density anywhere in space. So...how far out does your integral have to go?

charge density is, $$p = Q \alpha^2 e^{-\alpha r}}/(4 \pi r)$$ so I am thinking infinity which the intergral is undefined there

Assuming your charge density is correct (I think it is), the problem with the integral is not the limit at infinity, it's the limit at zero. I believe that if you start the integral at some radius b, you get a gamma function for the result. That's why I was initially wondering if the potential was good for all values of r.

I'm not suggesting that you don't learn to integrate, but I was never that great at it, so I'm glad things like this are on the internet.

Last edited by a moderator:
OlderDan,

But won't there be a differential volume element r^2dr?

## 1. What is total charge potential by line interaction?

Total charge potential by line interaction refers to the overall charge present in a system or substance due to the interaction between different charged particles or lines.

## 2. How is total charge potential by line interaction measured?

Total charge potential by line interaction is typically measured using instruments such as electrometers or voltmeters, which can detect and quantify the presence of electrical charge in a substance or system.

## 3. What factors can affect total charge potential by line interaction?

The amount and distribution of charged particles, the distance between them, and the type of material or medium they are interacting in can all affect the total charge potential by line interaction.

## 4. How is total charge potential by line interaction used in scientific research?

Total charge potential by line interaction is a fundamental aspect of many scientific fields, including physics, chemistry, and biology. It is often used to understand and study the behavior of charged particles, as well as to develop new technologies and materials.

## 5. What are some real-life applications of total charge potential by line interaction?

Total charge potential by line interaction has many practical applications, such as in the development of electronics and circuitry, in medical treatments like electrotherapy, and in environmental monitoring and control of air and water pollution.

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