# Gauss problem

1. Jan 22, 2007

### gazepdapi1

I can't figure out how to get started on this problem. Maybe you guys can help. A spherical ballon carries a total cahrge Q(1C) uniformly distributed over the surface. At t=0, r=r(sub 0), at t=30s, r=2r(sub 0). Find what is the electron field at 90 s at a distance of .5m from the ballon surface. I have to use Gaussean for this problem. I know that you have to get an expression for E(t), the electric field as a function of time. Can you guys help?
thanks
nertil

2. Jan 22, 2007

### Hootenanny

Staff Emeritus
Welcome to the forums,

For future reference, could you please post all homework questions in the appropriate forum, thanks.

With respect to your current question, can you write down a mathematical expression of Guass' law? Can you also write an expression for the area A of the balloon at time t?

3. Jan 22, 2007

### gazepdapi1

Gausses law
E=kQr/R^3, for a sphere where r is the radius of the imaginary Gauss sphere in the balloon and R is the radius of the ballon. The Surface area of the balloon as a function of t is SA(t) = 4(pi)r^2t. I don't know if thats correct or not. And sorry about the post location. I didn't realize.
thanks

4. Jan 22, 2007

### Hootenanny

Staff Emeritus
Ahh, you've skipped a few stages ; now that we have the electric field of a sphere, all we need to consider now is how the radius changes with time.

5. Jan 22, 2007

### gazepdapi1

thats where im stuck. I don't know how to relate the two.

6. Jan 23, 2007

### Hootenanny

Staff Emeritus
Okay, if we assume that the radius of the balloon increases linearly then we can say that r(t) = r0+ar0t = r0(1+at) , where a is some positive constant. From the conditions we have;

$$r(30)=r_{0}\left(1+30a\right) = 2r_{0} \Rightarrow 1+30a = 2\Rightarrow a = \frac{1}{30}$$

$$\therefore r(t) = r_{0}\left(1+\frac{t}{30}\right)$$

Can you go from here?