Assume a square charged plate (of almost zero thickness) with sides of length a ,lying entirely in the r - y plane, and containing ps Coulombs of positive charge per unit area, as shown in the figure below. ps (a) Find the r-component of the electric field as a function of position z along the z-axis (where r, y = 0). (b) Find the y-component of the electric field as a function of position z along the z-axis (where r, y=0). (c) Find the z-component of the electric field as a function of position z along the z-axis (where r, y = 0). (d) In your result for part (e) take the limit that the size of the plate is much much larger than the distances z that you are interested in (in other words, you are trying to find a formula for the z-component of the electric field for distances z real close to the charge plate). What is the answer? This integral may be useful: dy -a/2 (y2 +22)Vy2 y2+z2+42 áz (1 – tan--4a2zV2a+432