What is the charge carried by each sphere?

C is defined as 

C = Q/V where Q = charge stored and V = potential difference. 

Let's us Gauss' Law to find the charge on teh inner sphere since that is the only one that can contribute to the electric field between the spheres. Since the gaussian surface is a sphere of radius r where a < r < b, a = 5 cm and b =10 cm, Gauss' law gives: 

E = kQ/r^2 

The potential V = Integral[a,b](-E*dr) = kQ/r [a,b] = kQ(1/a - 1/b) = kQ( (b-a)/ab) 

Then C = Q/V = Q/kQ( (b-a)/ab) = ab/(k*(b-a)) = 4*pi*e0*ab/(b-a) 

Plug in converting cm --> m to get C 

Once you have C, then Q = CV where V = 100 V

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