Physics 230 Feb 20 2002
 
  Problem: The elecric potential 10 cm from the surface of a charged sphere of radius 10 cm is 1 kV. What is the total charge Q on the sphere?
 

The field-line diagram shows that the field outside the sphere is just like a point charge electric field.  It doesn't matter whether the charge is on the surface or distributed throughout the sphere- the field outside is the same either way. Thus the potential is also described by the same formula as for a point charge.  With reference point at infinity, we have:

V=kQ/r
Solving for the charge:
Q=Vr/k=(1x103 V)(0.2 m)/9x109 N.m2/C2
=2x10-8 C.
Check the units: A volt is a joule/coulomb = N.m/C , thus:
V.m.C2/N.m2 = C.