An insulator in the shape of a spherical shell is shown. The insulator is defined by an inner radius a = 4 cm and an outer radius b = 6 cm and carries a total charge of Q = +9 microC. You may assume that the charge is distributed uniformly throughout the volume of the insulator. What is Ey, the y-component of the electric field at point P which is located at (x, y) = (0, -5 cm)?
Volume of a sphere: 4/3pi R^3
Electric Field: E=4pi*r^2 = Qen / sigma o
Rho = total charge / total shell volume
Electric field at point P = rho * volume with charge
The Attempt at a Solution
Consulted my physics prof on this, but I am still not getting the correct answer (is an interactive online problem that says "OK" or "NO"). He told me to calculate the volume of the sphere, which was .000637 due to the large hole in the middle (volume only applicable to an area between r = 4 cm and r = 6 cm). Calculated rho to be 0.014135 based upon a total charge of +9 micro Coulombs...is this where I'm going wrong? Based upon the answer I received for rho, I multiplied it by the volume of the area between 4 and 5 cm, which I thought was represented by the formula 4/3 pi r^3. That gave me an answer of 5.92085 e -08 for the electric field. There is no x-component and the point lies on the y-axis, so no angle is considered. I tried using both a positive and negative value and cannot get a happy little "OK". Where did I go wrong? Please help!!!