Question

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

Answer 1

Electric field between two parallel plates

1. If infinitely large conducting plates are placed parallel to each other homogeneous electric field can be created.
2. This principle is used in parallel plate capacitors.
3. If charge carried by both plates is same then the electric field in the space between plates is equal to zero.
4. If the plates carry opposite charges then the charges repel each other, creating two oppositely directed electric fields in the space in-between the two plates.

Step - 1: Given data:

• The surface charge density on the plates is $\sigma =26.4\times {10}^{-12}C/m^2$
• The permittivity of free space is ${\epsilon }_0=8.854\times {10}^{-12}{C}^2/N-m^2$

Step -2: Formula used:

Suppose we have two plates are separated by distance $d$ and having charge densities $+\sigma$ and $-\sigma$ then electric field produced is, $E=\frac{\sigma }{{\epsilon }_0}$

Step - 3: Calculating the electric field:

$$\begin{gathered} TheelectricfieldbetweentwoparallellargeplatesisE=\frac{\sigma }{{\epsilon }_0} \\ =\frac{26.4\times 10-12}{8.854\times 10-12} \\ =2.98~3N/C \end{gathered}$$

Therefore the electric field between two parallel plates is 3 N/C (newton per coulomb).