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!

Calculate the electric potential of a sphere

  1. Nov 6, 2016 #1
    1. The problem statement, all variables and given/known data
    A metal sphere of radius ##a=1cm## is charged with ##Q_a=1nC##. Around a sphere is placed a spherical shell of inner radius ##b=2cm## and outer radius ##c=3cm##. The electrical potential of the shell in refenrence to a point in the infinity is ##V=150V##. The spheres are in a vacuum. Calculate:
    a) The electric potential of the inner sphere in reference to a point in the infinity
    b) The total charge of the spherical shell
    2. Relevant equations
    3. The attempt at a solution

    Im gonna give you the results straight away so you can help me faster.
    a) ##600V##
    b) ##-0.5nC##
    The first one i dont know how to start but the b) part i tried like this:
    ##V=\frac{Q}{4πξ_oR}## where ##R=C## and got 0.5 but i dont get the ##-## part. I dont understand this problem..Can you help?
     
  2. jcsd
  3. Nov 6, 2016 #2

    I like Serena

    User Avatar
    Homework Helper

    Hi doktorwho! :oldsmile:

    For (b) you calculated the total enclosed charge, which is indeed +0.5 nC. Since the inner sphere carries 1 nC, the outer spherical shell must have -0.5 nC.
     
  4. Nov 6, 2016 #3

    hilbert2

    User Avatar
    Science Advisor
    Gold Member

    If the sphere and the shell are made of metal (a conductor), the electrical potential is constant in them. Use Gauss's law to determine the electric field at different radii between the sphere and the outer shell, and then integrate to find the potential difference between the sphere and the shell.
     
  5. Nov 7, 2016 #4
    Can i do it like this?:
    ##V_a+∫Edl+V_c=V_{inner}##
    Basically im adding up the potential of the sphere at surface, the potential difference between point b and point a and the potential of the whole. Simply:
    ##V_b+V_c=V_{inner}## where i use the respective Q-s. Since the potential of the ##V_c=\frac{0.5}{4πε_or_c}## and the ##V_b## is proportional to ##V_c## ##V_b=2*\frac{3}{2}*V_c=450V## i get 600. Is this correct thinking?
     
  6. Nov 7, 2016 #5

    hilbert2

    User Avatar
    Science Advisor
    Gold Member

    ^ yes, that seems to be correct.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted