# Homework Help: Question on Gauss's Law

1. Feb 13, 2010

### Soulis

1. The problem statement, all variables and given/known data
A charge of 9 pC is uniformly distributed
throughout the volume between concentric
spherical surfaces having radii of 1.8 cm and
3.8 cm.

Let: Ke = 8.98755 × 109 N · m2/C2 .
What is the magnitude of the electric field
2.9 cm from the center of the surfaces?

2. Relevant equations
Electric Flux: (Ie) = E*A = q/epsilon
Electric Field: E = Ke*q/r^2

where A = Surface Area of gaussian sphere, and epsilon is a constant = 8.8542e-12

3. The attempt at a solution
My approach to this problem was assuming their was an inner charge at the center, which I labeled q. To start I used the formula for net flux Ie (electric flux) = E*A = q/epsilon. I neglected the outer sphere completely and used the principle that E (the electric field) is the electric field just outside the conductor and let that equal the charge given in the problem, and epsilon is a constant equal to 8.8542e-12, and A is the surface area of the inner sphere of radius .018m.

E = 9 pC (9e-12)
A = 4pi*r^2 = .004071504079
q = ?
epsilon = 8.8542e-12

Solved for q (my theoretical inner charge)

I used this equation to find my theoretical inner charge of the inner sphere (q) and then applied the generic formula for an electric field at a point P created by a charge q, E = Ke*q/r^2 to solve for the Electric field at P(a distance r from q).

Ke = 8.98755e+9
q = 3.244492027e-25 (answer from first part)
r = .029m

Using this approach I came out with E=3.467304913e-12, which needless to say, was incorrect. I feel I may have overcomplicated this problem and am approaching it incorrectly. Any help would be greatly appreciated, thanks.

2. Feb 13, 2010

### ehild

Can you formulate Gauss' Law?

ehild