Solve Gauss's Law: 8.0 & -4.9 Charges in Uncharged Sphere

[bmandude156]

Homework Statement

A 8.0 charge and a -4.9 charge are inside an uncharged sphere.
What is the electric flux through the sphere?

Homework Equations

It says in the book that Electric flux = E(4piR^2) although I do not know the radius and yet still don't believe that's the way to go to solving this problem.

The Attempt at a Solution

I attempted to add the charges together because I had no other idea what to do with them. And then tried to use the equation of a sphere for electric flux which is above. I do not know for sure if that is the way to proceed but I did not get the answer correct.

 

[sgd37]

you don't need the radius that's the point of gauss's law. Just substitute coulombs law for the electric field i.e. $$\frac{q}{4 \pi \epsilon_0 r^2}$$ into your equation for flux

 

[bmandude156]

I have immediate reservations after seeing your reply for i still see r^2 in your denominator. Isnt that going to be a problem and as for the charges, should I merely take the sum of them to be my q.

 

[betel]

sgd is talking about the electric field. You have to do something to it to get the electric flux.

 

[bmandude156]

i believe the equation at the moment is Electic flux = q/4piEnotr^2. by doing something I think ur implying..doing something to get rid of r^2. but i haven't a clue how or if that's what ur suggesting i do. sgd said that i didnt have to worry about r anymore but that's not true. coloumbs law had one itself. I am confused

 

[betel]

What are the quantities entering the formula for the electric flux. Your last formula is not correct.

 

[bmandude156]

well now I am more confused than ever. sgd gave me the formula. so r u saying that his formula was wrong.

 

[kaksmet]

In your first formula, you have the electric field, E, on the right hand side. See if you can use sgd37 formula for the electric field to calculate your flux.

 

[betel]

Do you know the difference between electric field and electric flux?

 

[bmandude156]

electric flux=E(4piR^2) and Electic flux = q/4piEnotr^2(was sgd's equation). now, what i think ur saying is take sgd's equation of electic flux and put it into mine. so the result is as follows: E(4piR^2) = q/4piEnotr^2. what i hoped would happen is by doing this, is alregbriaclly get rid of R. but i don't think that could happen. and for that matter...what is E now?!?...im afraid this is diogn more harm than good

 

[betel]

Perhaps you should first think about the equations and not randomly plugging one into the other that has the same letters in it.

 

[bmandude156]

you don't need the radius that's the point of gauss's law. Just substitute coulombs law for the electric field i.e. $$\frac{q}{4 \pi \epsilon_0 r^2}$$ into your equation for flux

. I am must be misunderstanding what the equation looks like than

 

[betel]

I have to repeat my question.

Do you know the difference between electric field and electric flux?

We can continuer argueing forever but if you don't know the difference we will get nowhere.

 

[bmandude156]

Electric flux is proportional to the number of electric field lines going through a surface. NO arguing here mate. just need help. electric field is like the magnetic field that pertains to charges attraction with each other

 

[betel]

Well, that is good.
Now what does Gauss's Law state? You already refer to it in the title, so why don't you do it the easy way?

 

[bmandude156]

Electric flux = E(4piR^2)..that one? But there was a problem with it remember...r^2?

 

[betel]

Now what is E in that formula?

Maybe Gauss's law in words is easier here.

 

[bmandude156]

electric field...sorry it took so long for me to respond...didnt see ur response on tihs page

 

[betel]

And the formula for the electric field is?

 

[bmandude156]

E=F/q

 

[betel]

I'm not sure what your F and q are but this formula seems strange.

 

[bmandude156]

hahah right from the book in my previous chapter. what is urrr formula for the electric field so we can progress?

 

[betel]

Then tell me what F and q are supposed to mean. I dont't know every definition of every book by heart and without that letters are meaningless.

And btw. I dont' have to solve this question.

 

[bmandude156]

F is the electric force and q is as usual, the charge. perhaps this isn't the proper equation seeing as ur unfamiliar with it

 

[betel]

Well it is not exactly the equation that will be of much help to us.

Didn't you derive a formula for the electric field of a point charge? I.e. if you have a charge q at radius r, what is the strength of the electric field?

And I still think you should have a statement of Gauss's law in words. This would kill this question in one go.

 

[bmandude156]

I will try to reply to ur post ASAP and i appreciate ur post. But ironically, I have a physics class at the moment. brb later

 

[sgd37]

wow this is one funny thread

so for the sake of my sanity; denoting electric FLUX with the Letter $$\Phi$$ and the electric FIELD as $$E$$

Now $$\Phi = E 4 \pi r^2$$ and $$E = \frac{q}{4 \pi \epsilon_0 r^2}$$

Substituting for $$E$$ in $$\Phi$$ you have

$$\Phi = \frac{q 4 \pi r^2}{4 \pi \epsilon_0 r^2} = \frac{q}{ \epsilon_0}$$

This is Gauss's law that the flux through a surface is the charge encompassed by that surface divided by the vacuum permittivity

 

[bmandude156]

ALRIGHT SO... what about the two charges. should i just sum them

 

[sgd37]

yeah

 

[bmandude156]

...but that didnt work good sir. the answer was incorrect. i got 3.5 X 10^-11.