1. Not finding help here? Sign up for a free 30min 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!

Work done in electrostatics

  1. Jan 9, 2016 #1
    1. The problem statement, all variables and given/known data
    A metallic sphere is placed inside a hollow spherical shell. The potential on the inner and outer spheres is 10 V and 5 V respectively. What is the potential at the center?(The spheres are concentric.)

    2. Relevant equations
    $$V =\frac{kq}{r}$$

    3. The attempt at a solution
    The obvious answer I thought of was 15 V. But the answer in my text was 10 V. I know that it would be 15 V in case of two concentric spherical shells. Does having a metallic sphere make a difference?(I don't think so because for a metallic sphere the charge resides on the surface.)
     
  2. jcsd
  3. Jan 9, 2016 #2

    gneill

    User Avatar

    Staff: Mentor

    What would happen if the potential inside the metallic sphere were different from the potential at its surface?
     
  4. Jan 9, 2016 #3
    how did you calculate 15 V?
     
  5. Jan 9, 2016 #4
    Then some work would be done in bringing the charge from the surface of the metallic sphere to its center. But I don't see how that could be the case.
     
  6. Jan 9, 2016 #5
    That's quite simple. You can just assume some quantity of charge on the spheres and then assume that the charges are concentrated at the center. That would yield the work done and the potential easily.
     
  7. Jan 9, 2016 #6

    gneill

    User Avatar

    Staff: Mentor

    Would the charge carriers in the metallic sphere remain static (stationary, unmoving) if the potential varied anywhere on or in it? Isn't this a problem in electrostatics?

    And I don't see the connection between your thread title and your problem statement. You haven't introduced any mechanism where work will be done, or gone through the exercise of calculating the work required to move a charge from infinity to the center. As far as I can tell you just guessed at an answer (15 V).
    How do you know this? Can you demonstrate?
     
  8. Jan 9, 2016 #7
    Maybe you summed both the potentials.. it's okay. For a metallic sphere potential at any place is same as to the surface. But is it same for a hollow sphere? I am not sure. You may do one thing, be sure about this point first then cone to the rest part.
     
  9. Jan 9, 2016 #8

    cnh1995

    User Avatar
    Homework Helper

    Can you find the equipotential part in this system?
     
  10. Jan 9, 2016 #9
    The potential is constant inside a hollow sphere.
     
  11. Jan 9, 2016 #10

    cnh1995

    User Avatar
    Homework Helper

    When there is net charge present on the sphere, potential due to that charge inside that sphere is constant everywhere.
     
  12. Jan 9, 2016 #11
    Doesn't it follow from the superposition principle?
     
  13. Jan 9, 2016 #12
    Doesn't this follow clearly from the superposition principle?

    Yes. I used the fact in this case.
     
  14. Jan 9, 2016 #13

    cnh1995

    User Avatar
    Homework Helper

    Consider this situation. There is a charge +q on the surface of the inner sphere and outer sphere is neutral. The potential of outer sphere is kq/r=5V. What will be the potential at the center then?
     
  15. Jan 9, 2016 #14
    $$5 + \frac{kq}{r_i}$$ ?
     
  16. Jan 9, 2016 #15

    cnh1995

    User Avatar
    Homework Helper

    Charge is on the surface of the inner sphere. What will be the potential at it's center then?
     
  17. Jan 9, 2016 #16

    gneill

    User Avatar

    Staff: Mentor

    If it is properly applied, yes. But you haven't shown how you applied it to arrive at a 15 V potential inside the 10 V sphere.
     
  18. Jan 10, 2016 #17
    $$\frac{kq}{r}$$

    I simply added the potential due to the two spheres.
     
  19. Jan 10, 2016 #18

    cnh1995

    User Avatar
    Homework Helper

    When the charge is on the surface of the sphere, potential at the surface and inside the sphere is same. The sphere is at 10V potential. Potential inside the sphere everywhere should be same. This implies E field inside the sphere is 0.
     
  20. Jan 10, 2016 #19
    So?
     
  21. Jan 10, 2016 #20

    cnh1995

    User Avatar
    Homework Helper

    So, the potential at the center will be equal to the potential of the inner sphere, won't it? The inner sphere is at 10V. So the potential at the center is also 10V.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Work done in electrostatics
Loading...