Walker, Halliday & Resnick — Electric Fields: Problem 57

57 Figure 22-48 shows a proton (p) on the central axis through a disk with a uniform charge density due to excess electrons. The disk is seen from an edge-on view. Three of those electrons are shown: electron \(e_c\) at the disk center and electrons \(e_s\) at opposite sides of the disk, at radius \(R\) from the center. The proton is initially at distance \(z = R = 2.00\text{ cm}\) from the disk. At that location, what are the magnitudes of (a) the electric field \(\vec{E}_c\) due to electron \(e_c\) and (b) the net electric field \(\vec{E}_{s,net}\) due to electrons \(e_s\)? The proton is then moved to \(z = R/20.0\). What then are the magnitudes of (c) \(\vec{E}_c\) and (d) \(\vec{E}_{s,net}\) at the proton's location? (e) From (a) and (c) we see that as the proton gets nearer to the disk, the magnitude of \(E_c\) increases, as expected. Why does the magnitude of \(E_{s,net}\) from the two side electrons decrease, as we see from (b) and (d)?