Maximum charge and voltage on a sphere

1. Jan 30, 2012

shyguy79

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. Jan 30, 2012

SammyS

Staff Emeritus
2cm = 0.02m , not 0.2m

3. Jan 30, 2012