Two spheres with uniform surface charge density, first with a radius of 7.5 cm and the second with a radius of 4.7 cm, are separated by a center-to-center distance of 33 {\rm cm}. The spheres have a combined charge of + 55\mu {\rm{C}} and repel one another with a force of 0.73 N. Assume q_1>q_2.
What is the surface charge density on the first sphere?
What is the surface charge density on the second sphere?
Iby K
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for point charges we can use F=k*q1*q2/r^2
(but since size of spheres is not negligible, problem is more complicated)
my guess is that we are expected to treat them as point charges, but express charges in terms of surface density.
q1+q2=55uC
r=0.33m
r^2=0.1089m^2
k=9*10^9
F=0.73N
F=k*q1*q2/r^2
q1*q2=F*r^2/k
q1*(55uC-q1)=0.73*0.1089/9*10^9
-q1^2+55*10^-6*q1-0.000000000008833=0
a=-1
b=0.000055
c=-0.000000000008833
then solve quadratic equation:
q1=[-b+(b^2-4ac)]/(2a)
or
q1=[-b-(b^2-4ac)]/(2a) (but this one will not work since both q1 and q2 must be positive)
then find q2:
q2=55uC-q1
to get surface charge, first find surface A of the sphere
then charge density is
p1=q1/A
p2=q2/A