Answer
$\frac{\sigma_1}{\sigma_2} = 2$
Work Step by Step
In part (b), we found that the charge on sphere 1 is $\frac{q}{3}$
In part (c), we found that the charge on sphere 2 is $\frac{2q}{3}$
We can find $\sigma_1$:
$\sigma_1 = \frac{q/3}{4\pi R_1^2} = \frac{q}{12\pi R_1^2}$
We can find $\sigma_2$:
$\sigma_2 = \frac{2q/3}{4\pi (2.00R_1)^2}$
$\sigma_2 = \frac{2q}{12\pi (4.00R_1^2)}$
$\sigma_2 = \frac{q}{24\pi R_1^2}$
We can find $\frac{\sigma_1}{\sigma_2}$:
$\frac{\sigma_1}{\sigma_2} = \frac{\frac{q}{12\pi R_1^2}}{\frac{q}{24\pi R_1^2}}$
$\frac{\sigma_1}{\sigma_2} = \frac{24}{12}$
$\frac{\sigma_1}{\sigma_2} = 2$
