Answer
The fraction of $q$ that ends up on sphere 2 is $~~\frac{2}{3}$
Work Step by Step
$V_1 = \frac{q_1}{4\pi~\epsilon_0~R_1}$
$V_2 = \frac{q_2}{4\pi~\epsilon_0~(2.00R_1)}$
Note that $V_1 = V_2$ and $q_1 = q-q_2$
We can find $q_2$:
$V_1 = V_2$
$\frac{q_1}{4\pi~\epsilon_0~R_1} = \frac{q_2}{4\pi~\epsilon_0~(2.00R_1)}$
$2.00~q_1 = q_2$
$2.00~(q-q_2) = q_2$
$3.00~q_2= 2.00q$
$q_2= \frac{2q}{3}$
The fraction of $q$ that ends up on sphere 2 is $~~\frac{2}{3}$.
