# Question about why they didnt integrate flux

• leonne
In summary, the students attempted to find the total charge enclosed in a sphere with radius R, but were not able to find the answer using Gauss' Law. Instead, they used a different equation that I am not familiar with.
leonne

## Homework Statement

find total charge in a sphere with radius R

## Homework Equations

integral with a circle in the middle( think its flux idk)) $$\int$$ Eda=Q/eo

## The Attempt at a Solution

so i got and in the solution eo $$\int$$ (kR^3 r^) (4 pie R^2)r^

for the answer they got eo(4pie kR^5) why didn't they get like 4/5(pie)(k)(R^4)they just combined it and didn't do any integration am i missing something here?

leonne said:

## Homework Statement

find total charge in a sphere with radius R

A complete problem statement would be useful. For that matter, when communicating acedimically or professionally, it is a good idea to use complete sentences . If others don't understand your work because of poor communication, what good is it? If others don't understand your question because of poor communication, how are they to answer you?

Anyways, I assume you are given either the electric field or charge density? What is it?

## Homework Equations

integral with a circle in the middle( think its flux idk)) $$\int$$ Eda=Q/eo

The $\LaTeX$ code for "integral with a circle in the middle" is \oint:

$$\oint\textbf{E}\cdot d\textbf{a}=\frac{Q_{\text{enclosed}}}{\epsilon_0}$$

This is Gauss' Law in integral form. It is one of the fundamental laws of Classical Electrodynamics, and it is worth remembering it's name (Gauss' Law can also be written in differential form $\mathbf{\nabla}\cdot\textbf{E}=\frac{\rho}{\epsilon_0}$ ).

## The Attempt at a Solution

so i got and in the solution eo $$\int$$ (kR^3 r^) (4 pie R^2)r^

I have no idea what you are trying to say here. Are you perhaps in possession of a solution manual for your text (say Griffiths Introduction to Electrodynamics)? If so, you might want to keep in mind that simply reading of solutions to problems isn't going to help you understand the concepts or master the problem solving skills needed to solve the problems yourself. Try solving the problem yourself before checking the solution. If you get stuck, post your attempt and we'll help you out.

for the answer they got eo(4pie kR^5) why didn't they get like 4/5(pie)(k)(R^4)they just combined it and didn't do any integration am i missing something here?

Again, try the problem...what surface are you integrating over if you want to find the total charge enclosed in a sphere of radius $R$ (centered at the origin?) ? What is the differential area element for that surface? What is the outward normal to that surface?

lol ok thanks for the info ill try it out again. My professor used a different formula q=$$\int$$pdv so was wondering about this one.

## 1. Why is flux integration important in scientific research?

Flux integration is important because it allows scientists to measure the flow of a substance or energy through a given area or volume. This information is crucial in understanding various natural processes and can help in predicting future changes.

## 2. What is the difference between flux integration and flux analysis?

Flux integration involves calculating the total amount of a substance or energy flowing through a given area. On the other hand, flux analysis focuses on studying the patterns and dynamics of flux over time and space.

## 3. Can flux integration be applied to different scientific fields?

Yes, flux integration can be applied to various scientific fields such as ecology, meteorology, geology, and oceanography. It is a versatile tool that can provide valuable insights in many different areas of research.

## 4. What are some common techniques used for flux integration?

Some common techniques for flux integration include flux chambers, eddy covariance, and remote sensing methods. Each technique has its advantages and limitations, and the choice depends on the specific research question and environmental conditions.

## 5. How can errors in flux integration be minimized?

To minimize errors in flux integration, it is important to carefully select the appropriate technique, calibrate instruments, and consider potential sources of error, such as changes in environmental conditions. Additionally, conducting multiple measurements and statistical analyses can help to improve the accuracy of results.

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