Question

Part A A solid sphere of radius R carries volume charge density ρ-Poer/R, where Po is a constant and r is the distance from the center. Find an expression for the electric field strength at the sphere's surface. Your expression should be in terms of the given variables and any other known variables such as the dielectric constant, eo. Eo is typed as "epsilono" without the quotations. Po is typed as "rhoo" without the quotations. poR E(R) rho0*(e-2)*R/epsilonoe 2) You are correct. Your receipt no. is 152-5716 (f) Part B Find an expression for the electric field for r>R.D E(r> R)- Submit Answer Incorrect. Tries 1/6 Previous Tries

A solid sphere of radius R...

I only need b) Find an expression for the electric field for r>R

Answer 1

Since the charge distribution is symmetric (i.e., it depends on 'n' only, rho = rho_0 e^n/R) , so the electric field only has rasial component . now, Gauss's law reads _s E middot d s = Q_enc/E_0, where Q_enc is the charge enclosed by the surface 's' . in our case we are taking the spherical surface s' , of radius r as the charge enclosed by this outer surface s' = charge enclosed in the inner sphere of radius R \r\n so, charge enclosed, i.e., total share contained in the sphere of posies R is, Q_enc = 4 pi integral^R_0 rho middot e^phi/R r^2 d r Implies Q_enc = 4 pi rho_0 [r^2 e^r/R/(1 ? R) - 2 r e^r/R/(1/R)^2 + 2 e^r/R/(1/R)^3]^R_0 Implies Q_enc = 4 pi rho_1 [R^3 e - 2 R^3 e + 2 R^3 e - 2 R^3] Implies Q_enc = 4 pi R^3 [e - 2] rho_0 now, contourintegral_s' E middot d s = Q_enc/E_0 since, E, the magnitude of electric