Answer
The net charge of shell A is $~~1.15\times 10^{-5}~C$
Work Step by Step
The flux is $-9.0\times 10^5~N~m^2/C$ when the enclosed charge within the Gaussian sphere is only the charge of the particle.
The flux is $4.0\times 10^5~N~m^2/C$ when the enclosed charge within the Gaussian sphere is the charge of the particle and the charge on shell A.
Therefore, the additional flux from shell A is $~~13\times 10^5~N~m^2/C$
We can find the net charge of shell A:
$\Phi = \frac{q}{\epsilon_0}$
$q = \Phi ~\epsilon_0$
$q = (13\times 10^5~N~m^2/C)(8.854\times 10^{-12}~F/m)$
$q = 1.15\times 10^{-5}~C$
The net charge of shell A is $~~1.15\times 10^{-5}~C$
