Solving Gauss' Law: Find Flux of 443C Ball with 7.97cm Radius

In summary, the website you got the question from may have incorrect calculations. Using Gauss' law, the flux passing through a surface is equal to the enclosed charge divided by the permittivity of free space. However, the website may be using the incorrect value for the permittivity of free space, leading to incorrect answers. It is important to double check the values and equations being used when solving these types of problems.
  • #1
delongk
18
0
How would you solve this:

A small charge of 443 C is at the center of a 7.97 cm radius ball. How much flux passes through the ball's surface?

The answer is 4.922 E-8 N.m2/C

I don't know how to get this answer. Please explain. Thank you!
 
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  • #2
You wrote the title as "Gauss Law Question". Do you know what Gauss' law says? Can you apply it here?
 
  • #3
I know it is Gauss' Law because that is what the website I got it from said. I have looked everywhere and applied the Gauss' Law how I thought I should apply it but I keep getting the wrong answer and have no idea how they got that answer. So that is why I need someone to explain it for me if they know.
 
  • #4
delongk said:
I know it is Gauss' Law because that is what the website I got it from said. I have looked everywhere and applied the Gauss' Law how I thought I should apply it but I keep getting the wrong answer and have no idea how they got that answer. So that is why I need someone to explain it for me if they know.
Perhaps if you showed your working we could point out where you have gone wrong...
 
  • #5
Well, I am confused as to what Gauss Equation to use... I have tried q=Eo*flux and then I tried flux=q/4pi*k and then I tried flux=k*q/r^2... none of them turn out correct.

What is the equation to use for a point charge in a sphere?
 
  • #6
I keep finding that flux= q/Eo and so I put 443 in for q and 8.85*10^-12 for Eo and get 5.006*10^13.
 
  • #7
Assuming that you are familiar with calculus, you can have a look at http://en.wikipedia.org/wiki/Gauss_law. The flux is indeed [itex]q/\epsilon_{0}[/itex] in your case :smile: Do you have a doubt about the flux being independent of [itex]R[/itex]? If so, the wiki article/a reading from any standard textbook should clear it.
 
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  • #8
443 C, is an awful lot of charge. Are you sure you got the numbers right from the question?

You calculated the flux as q_enc/Eo, and that should work.
 
  • #9
I copied and pasted it so I know that is right. And I keep getting the wrong answer for ALL of the examples... which are all similar to that one.
 
  • #10
Another example on the webpage is:

A small charge is at the center of a 9.77 cm radius ball. If 8.322 E-8 N.m2/C passes through the ball's surface, how much charge is at the center?

and the answer is 749C.

I don't get this one either. I am assuming the use the same equation.
 
  • #12
Ok, Gauss' law is

[tex] \int \vec{E}.d\vec{a} = \frac{q_{enc}}{\epsilon_0} [/tex]

That's the equation you're going to use for these problems.
Now, note that
(i) The value of [itex]\int \vec{E}.d\vec{a}[/itex] is the flux passing through the surface.
(ii) Using Gauss' law, it follows from the previous step that [itex]\frac{q_{enc}}{\epsilon_0}[/itex] is also the flux passing through the surface.
So, you've got 2 ways to calculate the flux.

Why have they given the radius? Because you can calculate the area of the ball. Notice that, when a charge is at the center of a sphere, the integral [itex]\int \vec{E}.d\vec{a}[/itex] can be simply reduced to E times A. Can you figure out why, and solve the problems from here?
 
  • #13
no i have no idea what to do... i need step by step. and everything i read said you don't need the radius.
 
  • #14
I think the problem is that whoever calculated the answers on that site is incorrectly using the Coloumb force constant {1/(4*Pi*epsilon_0)} instead of the permittivity of free space (epsilon_0) in their calculations. For instance, they ask this question:

"A small charge of 45 C is at the center of a ball. If 5 E-9 N.m2/C passes through the ball's surface, what is the radius of the ball (if it matters)? "

Now, obviously for that question the answer is that the radius doesn't matter, but if you use their values for charge and the flux, and plug into Flux = charge/k, solving for k you get 9x10^9, which is 1/(4*Pi*epsilon_0), not epsilon_0.

Also, if in the original question you asked, if you say Flux = 443/(9x10^9), you'll find you get their answer.

So, you were doing everything correctly; it's the website that is wrong.
 

1. What is Gauss' Law?

Gauss' Law is a fundamental law in electromagnetism that relates the electric flux through a closed surface to the total electric charge contained within that surface.

2. How do you solve Gauss' Law?

To solve Gauss' Law, you need to first define a closed surface and determine the total electric charge contained within that surface. Then, use the formula Q = ε0ΦE, where Q is the total charge, ε0 is the permittivity of free space, and ΦE is the electric flux, to find the electric flux through the surface.

3. What is electric flux?

Electric flux is a measure of the flow of electric field lines through a given surface. It is calculated by taking the dot product of the electric field and the surface area vector.

4. How do you find the electric flux of a specific object?

To find the electric flux of a specific object, you need to first determine the electric field at all points on the surface of the object. Then, calculate the dot product of the electric field and the surface area vector at each point and add them together to get the total electric flux.

5. Can Gauss' Law be used for objects with irregular shapes?

Yes, Gauss' Law can be used for objects with irregular shapes as long as the total electric charge contained within the surface can be determined and the electric field at all points on the surface can be calculated. However, for complex shapes, it may be more difficult to determine the electric field, making the application of Gauss' Law more challenging.

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