A charge of 100 C is evenly spread on a square plate of side 10 m and negligible thickness. What is the surface charge density?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 1\,\mathrm{C\,m^{-2}} \)
For charge spread evenly over a surface, the surface charge density is the charge per unit area, \( \sigma=Q/A \).
The area of the square plate is:
\( \begin{aligned} A &= a^{2} \\ &= (10\,\mathrm{m})^{2} \\ &= 100\,\mathrm{m^{2}} \end{aligned} \)
The surface charge density is:
\( \begin{aligned} \sigma &= \frac{Q}{A} \\ &= \frac{100\,\mathrm{C}}{100\,\mathrm{m^{2}}} \\ &= 1\,\mathrm{C\,m^{-2}} \end{aligned} \)