Question about why they didnt integrate flux

[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?

 

[gabbagabbahey]

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?

 

[leonne]

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.