Question

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total charge on the volune charge dsily Po of rdins o is centered at the origin Surrounding te entire systeensity is a PEC shell of inner radius b and outer radiusc lchare and metal shell) is Or a) Find the electric field vector in all four regions (r a. b) Find the surface change densities p, and p, on the surfaces c) Now assume that the metal shield is grounded. Give the new elec Psb and pae on electric field vector in all four regions (rsa,asrcb,bsrsc,r>c). d) After grounding, find the new surface change densities Psb and P on the surfaces r - b and Charge density Conducting shell

a.)

b.)

c.)

d.)

Answer 1

Radius of the sphere is a inner radius of the shell is b. outer radius of the shell is c. volume charge density of the sphere is rho_v_0 total charge of the sphere is Q = rho_v_0 times volume of the sphere Q = rho_v_0 times 4/3 pi a^3 (a) we draw a Gaussian surface of radius r (r < a) concentric with the sphere total charge in closed by the Gaussian surface is q_in = rho_v_0 times 4/3 pi r^3 \r\n from Gauss's law E.A = q_in/epsilon_0 E 4 pi r^2 = rho_v_0 times 4/3 pi r^3/epsilon_0 r E = rho_v_0 r/3 epsilon_0 r (radically outward direction) Now we draw a Gaussian surface of radius r (a < r < b) total charge in closed by the Gaussian surface is q_in = Q = rho_v_0 times 4/3 pi a^3 now from Gauss's law E 4 pi r^2 = q_in/epsilon_0 \r\n E 4 pi r^2 = rho_v_0 times 4/3 pi a^3/epsilon_0