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7. Consider a system of two infinitely-large plates with a finite thickness parallel to each other, as shown below. One plate is non-conducting and the other conducting. Each surface of the non-conducting plate is charged with the surface charge density $\sigma_1$ and $\sigma_2$, respectively. The other conducting plate is grounded. $\vec{E}_I$ $\sigma_1$ II Non-conducting $\vec{E}_{II}$ Gaussian surface S $\sigma_2$ III $\sigma$ $+\hat{z}$ IV Conducting $\vec{E}_{IV}$ We would like to find out the electric field in each region designated by I, II, III, and IV as well as the charge density $\sigma$ induced in the conducting surface. (a) Find out the induced charge density $\sigma$. Please write down $\sigma$ in terms of $\sigma_1$ and $\sigma_2$ (b) Please find out the electric field, $\vec{E}_I$, $\vec{E}_{II}$, $\vec{E}_{III}$, and $\vec{E}_{IV}$, in terms of $\sigma_1$, $\sigma_2$, and $\epsilon_0$. (c) A Gaussian surface S is shown in the figure. Show that Gauss's law is satisfied for this Gaussian surface.

          7. Consider a system of two infinitely-large plates with a finite thickness parallel to each other, as shown below. One plate is non-conducting and the other conducting. Each surface of the non-conducting plate is charged with the surface charge density $\sigma_1$ and $\sigma_2$, respectively. The other conducting plate is grounded.

$\vec{E}_I$
$\sigma_1$
II
Non-conducting $\vec{E}_{II}$
Gaussian surface S
$\sigma_2$
III
$\sigma$
$+\hat{z}$ IV
Conducting $\vec{E}_{IV}$

We would like to find out the electric field in each region designated by I, II, III, and IV as well as the charge density $\sigma$ induced in the conducting surface.
(a) Find out the induced charge density $\sigma$. Please write down $\sigma$ in terms of $\sigma_1$ and $\sigma_2$
(b) Please find out the electric field, $\vec{E}_I$, $\vec{E}_{II}$, $\vec{E}_{III}$, and $\vec{E}_{IV}$, in terms of $\sigma_1$, $\sigma_2$, and $\epsilon_0$.
(c) A Gaussian surface S is shown in the figure. Show that Gauss's law is satisfied for this Gaussian surface.

7. Consider a system of two infinitely-large plates with a finite thickness parallel to each other, as shown below. One plate is non-conducting and the other conducting. Each surface of the non-conducting plate is charged with the surface charge density σ1 and σ2, respectively. The other conducting plate is grounded.

E⃗I
σ1
II
Non-conducting E⃗II
Gaussian surface S
σ2
III
σ
+ẑ IV
Conducting E⃗IV

We would like to find out the electric field in each region designated by I, II, III, and IV as well as the charge density σ induced in the conducting surface.
(a) Find out the induced charge density σ. Please write down σ in terms of σ1 and σ2
(b) Please find out the electric field, E⃗I, E⃗II, E⃗III, and E⃗IV, in terms of σ1, σ2, and ϵ0.
(c) A Gaussian surface S is shown in the figure. Show that Gauss's law is satisfied for this Gaussian surface.

Added by Sean M.

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