Sheet on a sphere **

Consider a large flat horizontal sheet with thickness x and volume charge density ρ. This sheet is tangent to a sphere with radius R and volume charge density ρ0, as shown in Fig. 1.38. Let A be the point of tangency, and let B be the point opposite to A on the top side of the sheet. Show that the net upward electric field (from the sphere plus the sheet) at B is larger than at A if ρ > (2/3)ρ0. (Assume x « R.)

         figure 1.36

          figure 1.37

B          r

    figure 1.38