Halliday, Resnick & Walker — Gauss' Law: Problem 10

10 Figure 23-27 shows a very large nonconducting sheet that has a uniform surface charge density of \(\sigma = -2.00 \mu\text{C/m}^2\); it also shows a particle of charge \(Q = 8.00 \mu\text{C}\), at distance \(d\) from the sheet. Both are fixed in place. If \(d = 0.200 \text{ m}\), at what (a) positive and (b) negative coordinate on the \(x\) axis (other than infinity) is the net electric field \(\vec{E}_{\text{net}}\) of the sheet and particle zero? (c) If \(d = 0.950 \text{ m}\), at what coordinate on the \(x\) axis is \(\vec{E}_{\text{net}} = 0\)?