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Homework Help: What is the electric field around a conducting sphere?

  1. Nov 16, 2005 #1
    Hi all,
    I am having some troubles with some Electromagnetism questions. First of all can someone please explain the basics behind Electric fields. The question asks "What is the electric field around a conducting sphere of radius R carrying a charge Q". Does this imply that because the sphere is conducting that the charge is spread evenly and therefore can be considered as a point charge at the centre of the sphere? Does the use of Gauss's law help to get the correct answer, i.e

    E= q/(4 x pi x permittivity of free space x r^2)x the unit vector in the field direction

    I am slightly confused about this one.

    The next part of the question asks " What is the electric potential at the surface of the sphere if the potential infinately far away is zero". As far as I know the potential is essentially a 'band' where the electric field is constant, so therefore is the electris field at the distance of the sphere, and because infinately far away = zero then at the surface is simply minus the field strength?

    Please any explanation would be great. thanks
     
  2. jcsd
  3. Nov 16, 2005 #2
    First part sounds good:

    Potential from a point away from infinity is simply:
    [tex]V=\frac{kq}{r}[/tex],

    this is indirectly from coulombs law:

    [tex]E=\frac{kq}{r^2}[/tex]
    [tex]V=E\cdot r=\frac{kq}{r}[/tex]

    where [tex]k=\frac{1}{4\pi\epsilon_0}[/tex]

    Does this help you?

    Regards,
    Sam

    (Sorry about the mistake if anyone read it quick enough)!
     
    Last edited: Nov 16, 2005
  4. Nov 16, 2005 #3
    An important point with this, is to notice that V = E.r (scalar product), is a scalar quantity. I have made many mistakes in the past on this topic thinking that Voltage had a direction (whoops)! :smile:

    Note: I've left out the [tex]\cos\theta[/tex], oweing to the fact that the Electric field about a point charge (which this example can be considered), is radial.

    Regards,
    Sam
     
    Last edited: Nov 16, 2005
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