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Electric field conductor problem

I'm revising for my exam and got stuck in the following questions. Please help.

1) An isolated spherical conductor of radius r is charged to a potential V. The total electrical energy stored is _______.
This is an MC question and the answer is V2(2*pi*εo*r)
I only know energy stored = Qq/(4*pi*εo*r) and V=Q/(4*pi*εo*r)

2)A positively-charged metal sphere A of radius a is joined by a conducting wire to an uncharged metal sphere B of radius b placed far away from the first sphere. THe ratio of the surface charged density on sphere A to that on sphere B is ______.
The answer is b/a.

Well, I know surface area of A :surface area of B = a^2:b^2. How can I get the answer b/a ?

Thanks in advance.
 

HallsofIvy

Science Advisor
Homework Helper
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In the first problem you have an incorrect formula: this is an "isolated" conductor so you do NOT have two charges, q and Q.
Since you have only one charge, Q, you need to use
energy stored = Q2/(4*pi*epsilon*r).

You also know V=Q/(4*pi*epsilon*r) so Q= V/(4*pi*epsilon*r) and Q2= V2/(4*pi*epsilon*r)2. Substitute that into the first equation and then simplify.
 
That means the answer isn't V^2(2*pi*eplison*r) but V^2(4*pi*eplison*r). I'm pretty sure I was given a wrong answer.
Thanks.
 

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