The electric field on two sides of a large charged plate is shown in Fig. The charge density on the plate in S.I. Units are given by \(K \varepsilon_{0}\left(\varepsilon_{0}\right.\) is the permittivity of free space in S.I. Units), Find value of \(K\)

Question

Aicharya · Accepted Answer

From the figure it is clear that the plate is placed in an external electric field. Let the electric field due to the plate is \(\mathrm{E}\) and \(\mathrm{E}_{0}\) be the external electric field.
\(\begin{array}{l}
\therefore \mathrm{E}_{0}+\mathrm{E}=12 \mathrm{Vm}^{-1} \\
\mathrm{E}_{0}-\mathrm{E}=8 \mathrm{Vm}^{-1}
\end{array}\)
Solving equation, \(\mathrm{E}=2 \mathrm{Vm}^{-1}\) and
\(\mathrm{E}_{0}=10 \mathrm{Vm}^{-1}\)
Now, electric field due to plate \(=\frac{\sigma}{2 \varepsilon_{0}}=2\)
\(\therefore \sigma=4 \varepsilon_{0}\)

The electric field on two sides of a large charged plate is shown in Fig. The charge density on the plate in…

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