Question

Consider a wide, nearly flat square with uniform charge density p. The square is centered at the origin and is lying parallel to the xy plane. It has side length a and thickness h h<<a, so the top surface of the square is at z=h/2 and the bottom is at z=-h/2. Find a simple approximate (monomial) expression for the magnitude of the electric field on the z-axis for
(1). 0 < z < h/2

Consider a wide, nearly flat square with uniform charge density p. The square is centered at the origin and is lying parallel to the xy-plane. It has side length a and thickness h << a, so the top surface of the square is at z=h/2 and the bottom is at z-h/2.Find a simple approximate (monomial) expression for the magnitude of the electric field on the z-axis for 0 < z < h/2. (Hint: think separately about the fields from the part of the square below z and from the part of the square above z.) (Use any variable or symbol stated above along with the following as necessary: eo-) E(z) Find a simple approximate (monomial) expression for the magnitude of the electric field on the z-axis for h/2 < z <<a E(z) z Find a simple approximate (monomial) expression for the magnitude of the electric field on the z-axis for z>>a: E(z) * Sketch E(z) as a function of z, with z ranging from 0 to 100a. DO NOT DRAW THE Z-AXIS TO SCALE! Your z axis should have three roughly equally-sized regions corresponding to your three answers above (so you should have equally spaced, labeled ticks at z=h/2 and z=a). You should also have labeled ticks at the corresponding places on the E axis.

(2). h/2 < z << a

(3). z >> a

Answer 1

E vector = rho times 2z/z elementof_0 = rho z/elementof_0 k hat only thickness 2z responsible for electric field. E vector = rho times h/2 elementof_0 = rho h/2 elementof_0 k hat whole charge responsible for E vector for z > > a The will set as a point charge Therefore E vector = 1/4 pi elementof_0 (rho s^2 h)/z^2 k hat.