Question

Two parallel large thin metal sheets have equal surface charge densities $\left(\sigma =26.4\times {10}^{-12}\mathrm{c}/{\mathrm{m}}^2\right)$ of opposite signs. The electric field between these sheets is

• A. $1.5\mathrm{N}/\mathrm{c}$
• B. $3\mathrm{N}/\mathrm{c}$
• C. $1.5\times {10}^{-10}\mathrm{N}/\mathrm{c}$
• D. $3\times {10}^{-10}\mathrm{N}/\mathrm{c}$

Answer 1

The correct option is A

$1.5\mathrm{N}/\mathrm{c}$

Gauss's Law

1. Gauss's law states that the net flux in a closed surface is directly proportional to the electric charge.
2. The equation for the net flux can be written as follows:

$E=\frac{\sigma }{2{\epsilon }_0}$

Here, $E$ is the net flux, $\sigma$ is the surface charge density, and ${\epsilon }_0$ is the constant.

$$\begin{gathered} E=\frac{26.4\times {10}^{-12}\mathrm{c}/{\mathrm{m}}^2}{2\times 8.854\times {10}^{-12}{\mathrm{c}}^2/{\mathrm{Nm}}^2} \\ E=\frac{3\mathrm{N}/\mathrm{c}}{2} \\ E=1.5\mathrm{N}/\mathrm{c} \end{gathered}$$

Hence, the electric field between the sheets is $1.5\mathrm{N}/\mathrm{c}$.

Therefore, option (A) is correct.