A solid insulating sphere of radius a has a charge -q (q > 0) distributed unifor

Question

A solid insulating sphere of radius a has a charge -q (q > 0) distributed uniformly throughout its volume. It is surrounded by a thick spherical insulating shell of inner radius b and outer radius c. A charge 2q is distributed uniformly throughout the insulating shell.

(a) Derive expressions for the electricfield magnitude in terms of the distance r from the center for the regions r < a, a < r < b, b < r < c, r > c.
(b) Sketch the electric field lines in the regions a < r < b and r > c.
(c) Graph the electric field magnitude as a function of r.

Explanation / Answer

(a) r <a the electric field E = - k *q_enlosed / r^2 here q_enclosed = charge density * V here charge density = total charge / vloume the sphere V = volume enclosed by the gaussinn surface (4/3) r^3 (b) in the rigion a< r < b the elctric field E = - k*q / r^2 (c) in the rigion b< r< c Electric field    E = k*q_enclsed / r^2 here q_enclosed = charge density * V here charge density = (total charge of the shell (2q )) /( V_b - V_c) V_b = (4/3)b^3 and V_c = (4/3)c^3 V = volume enclosed by the gaussian surface = V_b - V_r V_r = (4/3)r^3 (d) for the region r> c Electric field E = k* (2q ) / r^2 the electric field lines a< r < b region direction from shell to shpere since the sphere carryies negative charge and shell carries positive charge In the region r < c the field lines out ward in direction

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