A metallic sphere A of radius 1.00 cm is several centimeters away from a metalli

Question

A metallic sphere A of radius 1.00 cm is several centimeters away from a metallic spherical shell B of radius 2.00 cm. Charge 450 nC is placed on A, with no charge on B or anywhere nearby. Next, the two objects are joined by a long, thin, metallic wire (as shown in the figure below), and finally the wire is removed. How is the charge shared between A and B?

My actual question is, I know you're supposed to do it using kq/r + kq/r = 0 for equal potential everywhere, but why can I not calculate uniform surface charge density (since it's equilibrium) and then take the ratios of each surface for it's charge?

Also, when do I use ratios for uniform density VS using equipotential?

Note: No conductance equations since course hasn't covered it yet

Explanation / Answer

We cannot do kq/r +kq/r=0 as none of the sphere is connected to earth so we cannot equate it to 0 volts .We can say that both will have same potential

Let charge on A is q and charge on B is Q

Q+q=450 nC

Kq/1=kQ/2

Q=2q

So Q=300 nC

q=150 nC

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