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Homework Help: Ratio of potentials and charges on two spheres

  1. Apr 13, 2008 #1
    1. The problem statement, all variables and given/known data
    Consider two "solid" conducting spheres with radii r1= 4 and r2= 1. I.E., r2/r1= 1/4.

    The two spheres are separated by a large distance so that the field and the potential at the surface of sphere #1 only depends on the charge on #1 and the corresponding quantities on #2 only depend on the charge on #2.

    Place an equal amount of charge on both spheres, q1=q2=Q.

    After electrostatic equilibrium on each sphere has been established, what is the ratio of the two potentials V2/V1 at the "centers" of the two solid conducting spheres?

    What is the ratio of the electric fields E2/E1 at the "surfaces" of the two spheres?

    2. Relevant equations
    As near as I can figure out:

    q= charge
    r= Displacement from the reference point in the direction of the field

    Delta V= Kc (q/r)

    E= Magnitude of the electric field
    d= Displacement

    Delta V= -E Delta d

    3. The attempt at a solution

    At first, I set the charge on each at 10 for the sake of convenience, than ran the numbers through the formula. I ended up with V1= 2.2475e10 and V2=8.99e10. When V2 was divided by V1, I ended up with a ratio of 4.

    As far as electric fields went, I ran the second formula and then divided E2 by E1 for a ratio of 16.

    Did I work this problem correctly?
  2. jcsd
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