Suppose that a charged particle is held at the center of two concentric conducting spherical shells \(A\) and \(B,\) as shown in the above figure. The radius of sphere \(A\) is \(r_A=2\text{ cm}\) and that of sphere \(B\) is \(r_B=4\text{ cm}.\) The net flux \(\Phi\) through a Gaussian sphere centered on the particle is \[\begin{align} -16.0 \times 10^5 \text{ N}\cdot\text{m}^2\text{/C} &\text{for } 0 < r < r_A \\ +8.0 \times 10^5 \text{ N}\cdot\text{m}^2\text{/C} &\text{for } r_A < r < r_B\\ -4.0 \times 10^5 \text{ N}\cdot\text{m}^2\text{/C} &\text{for } r > r_A, \end{align}\] where \(r\) is the radius of the Gaussian sphere. Then what are the net charges of shell \(A\) and shell \(B,\) respectively?

The value of the permittivity constant is \(\varepsilon_0=8.85 \times 10^{-12} \text{ C}^2\text{/N}\cdot\text{m}^2.\)