Question

Slab of charge. Consider the infinite sheet of charge again but this time suppose the sheet has thickness 2D. Suppose the slab has uniform posi- tive charge-per-volume ρ. (a) What is the field E midway between the two surfaces? (b) Find the field at a point inside the slab a distance a < D from the midpoint. (c) Find the field at a point outside the slab a distance b > D from the mid- point. (d) Sketch a plot of E vs r, where r is the distance from the middle of the slab, over the range 0 < r 2D. Hint: In (b) and (c), con- sider a gaussian pillbox with the point of interest on one cap and the other cap at the middle of the slab. You could also center the pillbox around the middle of the slab

Answer 1

(B) Gauss' law contourintegral_s E bar ds bar = Q_enc/epsilovariant_0 consider a plane surface of area A at a distance a from mid way plane place another identical plane at distance a on the other side join them with side walls This is our Gaussian surface S. By symmetry E bar perpendicularto ds bar on plane surfaces and E bar perpendicularto ds bar on side walls Also Vertical-bar E bar Vertical-bar is uniform on plane surfaces countourintegral_s E bar ds bar = integral_ends E bar ds bar + integral_sides E bar ds bar = 2 E A = 2 a A rho/epsilonvariant_0 E = rho a/epsilovariant_0, rightarrow \r\n on the right E bar = rho a/epsilonvariant_0 n on left E bar = -rho a/epsilonvariant_0 n (a) From result in (b) E bar (mid way between planes) is zero. (c) Consider a similar