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Maximum charge and voltage on a sphere

  1. Jan 30, 2012 #1
    Hi guys, doing an assignment question

    1. The problem statement, all variables and given/known data
    A spherical conductor filled with air with a radius of 2cm is supported in the air. Electrical breakdown occurs when the electric field reaches 3.0 x 10^6 Vm^-1

    (a) What is the maximum charge that can be placed on the sphere?
    (b) What is the value of the potential on the surface of the conductor when carrying maximum charge

    2. Relevant equations
    E(r) = 1/4∏ε0 x Q/R^2 where 1/4∏ε0 = 9x10^9, Q = charge and R^2 =radius of sphere 0.2m
    V(r) = 1/4∏ε0 x Q/R

    3. The attempt at a solution
    Ok, so for the (a) then using the equation for electric field E(r) rearranged for Q

    Q = (E(r) x R^2)/9x10^9 =(3.0 x 10^6 Vm^-1 x 0.2^2)/9x10^9 = 13μC

    Seems realistic? Just not sure of the next bit...

    V(r) = 1/4∏ε0 x Q/R = 9x10^9 x (13x10-6C / 0.2m) = 585kV

    585kV???????? Something has gone wrong.... is this a viable answer or should I be taking into account the area of the sphere...
  2. jcsd
  3. Jan 30, 2012 #2


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    2cm = 0.02m , not 0.2m
  4. Jan 30, 2012 #3
    Thanks for the heads up - that should have read

    spherical conductor filled with air with a radius of 20cm
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