Question

A charge of -5.37 nC is uniformly distributed on a thin square sheet of nonconducting material of edge length 23.4 cm. What is the surface charge density of the sheet? Tries 0/5 Problem 22-60b: What is the magnitude of the electric field next to the sheet and proximate to the center of the sheet?

Answer 1

$\text{Solution :}\\ \text{Surface charge density is expressed by :}\\ \sigma =\dfrac{Q}{A} = \dfrac{Q}{L^2} \\ \ \\ \text{Given :}\\ \text{Charge} \ Q = -5.37nC = -5.37\times 10^{-9}C\\ \text{Edge length of the square } L = 23.4\ cm = 0.234\ m \\ \text{Plugging in these values in the above equation, we get;}\\ \sigma = \dfrac{-5.37\times 10^{-9}C}{(0.234m)^2}= -9.8\times 10^{-8}C/m^2\\ \ \\ \ \\ \text{Electric field proximity to center of the square is:}\\ E = \dfrac{\sigma}{2\epsilon_o}\\ E = \dfrac{-9.8\times 10^{-8}C/m^2}{2\times (8.85\times 10^{-12} \ C^2/N.m)}\\ E = -5540.7\ N/C\\ \text{Magnitude } E = 5540.7\ N/C\\$