Question

The nestedspheres righa consist ofan iner metal sphere of radius a and charge demsity + a and a neutral outer metal spherical shell of inner radius b and outer radius c Mathematical Analysis a Find the total charge on the inner sphere b. Find the charge density at r b: c. Find the charge enclosed by a spherical Gaussian surface at rea

Answer 1

"As the inner sphere is metallic all of its charge will be an surface & so 'sigma' is the surface charge densuty therefore charge on inner sphere, q = sigma(4 pi a^2) Consider the gaussian surface (red dotted line) as shown: - phi = E(4 phi r^2) = q_inside/epsilon_0 therefore E = 0[everywher in metal] = > q_inside = 0 = > q_inner surface of shell + q_sphere = 0 = > q_inner surface of shell therefore sigma_b = - sigma(4 pi a^2)/4 pib^2 = - sigma a^2/b^2 Now as there was no charge on the shell initially so A/c to charge conservation principle shell wont also have any charge finally i.e, q_inner surface + q_outer surface = 0 = > q_outer surface = sigma(4 pi a^2) therefore sigma_c = sigma(4 pia^2)/4 pic^2 = sigma a^2/c^2 r < a: - q_enclosed = 0 a < r < b: - q_enclosed = sigma(4 pi a^2) b < r < c: - q_enclosed = 0 = sigma