Figure 23-47 shows cross-sections through two large, parallel, non-conducting sheets with identical distributions of positive charge with surface charge density$\mathbf{\sigma }\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{77}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{22}}\mathbf{C}\mathbf{/}{\mathbf{m}}^{\mathbf{2}}$. In unit-vector notation, what is the electric field at points (a) above the sheets, (b) between them, and (c) below them?

a) There are two parallel non-conducting sheets with identical charges.

b) The surface density,$\mathrm{\sigma }=1.77\times {10}^{-22}\mathrm{C}/{\mathrm{m}}^2$

Using the concept of Gauss law-planar symmetry, we can get the value of the electric field between, above, and below the non-conducting sheets.

Formula:

The electric field of a non-conducting sheet, $\mathrm{E}=\frac{\mathrm{\sigma }}{2{\mathrm{\epsilon }}_0}$ (1)

Using the superposition principle, the electric field present at points above the sheets is given using equation (1) as follows:

$$\begin{gathered} \mathrm{E}=\frac{\mathrm{\sigma }}{2{\mathrm{\epsilon }}_0} \\ =\frac{1.77\times {10}^{-22}\mathrm{C}/{\mathrm{m}}^2}{8.85\times {10}^{-12}{\mathrm{C}}^2/\mathrm{N}.{\mathrm{m}}^2} \\ =2.00\times {10}^{-11}\mathrm{N}/\mathrm{C} \end{gathered}$$

Hence, the value of the electric field is$2.00\times {10}^{-11}\mathrm{N}/\mathrm{C}$ , which is pointing in the upward direction.

According to the concept, the charge is present on the sheets, hence, the electric field using equation (1) is 0 N/C .

Using the superposition principle, the electric field present at points above the sheets is given using equation (1) as follows:

$$\begin{gathered} \mathrm{E}=\frac{\mathrm{\sigma }}{2{\mathrm{\epsilon }}_0} \\ =\frac{1.77\times {10}^{-22}\mathrm{C}/{\mathrm{m}}^2}{8.85\times {10}^{-12}{\mathrm{C}}^2/\mathrm{N}.{\mathrm{m}}^2} \\ =2.00\times {10}^{-11}\mathrm{N}/\mathrm{C} \end{gathered}$$

Hence, the value of the electric field is$2.00\times {10}^{-11}\mathrm{N}/\mathrm{C}$ , which is pointing in a downward direction.