Help Solving a Problem Involving Gaussian & Spherical Balloon Charge

[gazepdapi1]

I can't figure out how to get started on this problem. Maybe you guys can help. A spherical balloon 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 balloon 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

 

[Hootenanny]

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?

 

[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 that's correct or not. And sorry about the post location. I didn't realize.
thanks

 

[Hootenanny]

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.

 

[gazepdapi1]

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

 

[Hootenanny]

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?