Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to calculate electric charge with a given electric potential?

  1. Mar 31, 2013 #1
    Hi!

    An iron plate with a mass of 1 kg surrounded by vacuum has an electric potential of +20 kV. How do I calculate the charge, Q of the iron plate?

    I have all the information I need, right?
     
  2. jcsd
  3. Mar 31, 2013 #2
    You also need the shape of the plate (thickness, diameter). And I don't know if you are talking about self capacitance here or if the plate is near another plate.
    http://en.wikipedia.org/wiki/Capacitance#Self-capacitance
    The charge of the plate is the electric potential times it's capacitance.
     
  4. Mar 31, 2013 #3
    Thanks for your reply!

    The iron plate is not near another plate, so I'm talking about self capacitance.

    But I don't have the capacitance.

    Is the capacitance a value based on the shape and the electric properties of the material? How do I calculate it?

    Say that the shape of the 1 kg iron plate is a square with an area of 0.225 m^2. That makes the thickness 0.0025 m since the density of iron is 7874 kg/m^3.
     
  5. Apr 1, 2013 #4

    BruceW

    User Avatar
    Homework Helper

    It is going to be pretty complicated expression because it is not a highly-symmetric object. (For example, a sphere would give a nice answer). But for your problem, there is still an exact answer. Assuming the charges in the object are fixed, we than have the electrostatic equation:
    [tex]\nabla^2 \phi = - \frac{\rho}{\epsilon_0} [/tex]
    This is the 'exact answer' I was talking about. From here, it gets a bit complicated, because the charge distribution rho does not follow a simple symmetry. Of course, you could take the limit of some point near the surface of the object, in which case, you can get a simple (approximate) answer.
     
  6. Apr 1, 2013 #5
    Thanks for your reply Bruce, and happy Easter!

    Is there a difference in charge distribution for a positively charged object compared to a negatively charged object? The iron plate would be positively charged if that makes any difference.
     
  7. Apr 1, 2013 #6
    Did you look at the wikipedia page for self capacitance? For a circular disc it's approximatly 8εr. r is the radius of the disc and ε = 8.85× 10−12 F/m. The thickness doesn't matter as long as the radius is much bigger than the thickness. So a thin big plate will have a larger capacitance than a small thick one.
     
  8. Apr 1, 2013 #7

    BruceW

    User Avatar
    Homework Helper

    the only difference in the potential for a positively or negatively charged plate is that the sign of the potential would be opposite. (using the convention that the potential at infinity is zero). Also, DrZoidberg brings up a good point. (p.s. I'm a futurama fan too). I guess that for a circular disk, you can use a cylindrical coordinate system, and take the approximation that the disk is very flat, then I guess it is not too difficult to do the calculation. I have not done this calculation myself, but I would guess that is the general idea.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: How to calculate electric charge with a given electric potential?
Loading...