# Three parallel planes – calculating charge

1. The problem statement, all variables and given/known data
There are three parallel identical planes of area A = 200 cm^2, and the distance between the upper and the middle one as well as the distance between the middle and the lower one is d = 3cm. The upper plane was charged to q1 = 0.5 nC. The other two were connected to a V= 100V EMF source. Calculate the charges of the middle and lower planes.

2. Relevant equations
$V = E * d$
$E * A = q / \epsilon_0$

3. The attempt at a solution

I firstly assumed that after being connected to the source, the potential of the middle plane is 0 V, and the potential of the lower plane – 100V. Then from Gaus’s law, we find the electric field between the planes:
$E_{12} * A = \frac{q_1 + q_2}{\epsilon_0}$
$E_{23} * A = \frac{q_2 + q_3}{\epsilon_0}$
Where 1st, 2nd and 3rd planes are upper, middle and lower correspondingly.
Then
$V_{12} = E_{12}*d = \frac{(q_1 + q_2)*d}{\epsilon_0 * A}$
$V_{23} = 100 = E_{23}*d = \frac{(q_2 + q_3)*d}{\epsilon_0 * A}$
But here we have 3 unknowns and 2 equations… Are there any other ways to calculate $V_{12}$, for instance?

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