1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Spherical Shell using Gauss' Law

  1. Jun 21, 2016 #1
    1. The problem statement, all variables and given/known data
    An insulator is in the shape of a spherical shell. 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 mu.gif C (1 mu.gif C = 10-6 C). 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)?

    2. Relevant equations
    Φnet = Qenclosed / ∈0 = E × ∫surface dA

    3. The attempt at a solution
    I found the charge density ρ:
    Total charge 9e-6 C / ( 4/3 π (0.062 - 0.042)) = ρ

    Then, with my Gaussian surface a sphere with radius 5 cm, I found Qenclosed
    Qenclosed = ρV = ρ * 4/3 π (0.052 - 0.042)

    I know that
    Φnet = Qenclosed / ∈0 = E × ∫surface dA
    which I can rearrange such that
    E (this is what I need to find - the electric field on the surface) = Qenclosed / (ε0 * ∫surface dA)
    And since ∫surface dA = 4 π r2
    I can find E:
    E = 1/4πε0 * Qenclosed / r2 = 1/4πε0 * 4.05e-6 / 0.052 = 14563800

    This isn't correct, though. Where did I go wrong? I think it is in those last few equations - do I have the wrong area?

    The units do work out: k has units N*m2/C2, Qenc has units C, and r2 is in m2, which works out to N/C
  2. jcsd
  3. Jun 21, 2016 #2


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    Hello! Welcome to PF!

    Your expression for the volume of a sphere is not correct. The power of r is not right.

    Otherwise, your method looks good to me :smile:
  4. Jun 21, 2016 #3
    Oops! Thank you.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted