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A spherical shell has inner radius Rin and outer radius
Chapter 24, Problem 24.81(choose chapter or problem)
A spherical shell has inner radius Rin and outer radius Rout . The shell contains total charge Q, uniformly distributed. The interior of the shell is empty of charge and matter. a. Find the electric field strength outside the shell, r Rout . b. Find the electric field strength in the interior of the shell, r Rin. c. Find the electric field strength within the shell, Rin r Rout . d. Show that your solutions match at both the inner and outer boundaries.
Questions & Answers
QUESTION:
A spherical shell has inner radius Rin and outer radius Rout . The shell contains total charge Q, uniformly distributed. The interior of the shell is empty of charge and matter. a. Find the electric field strength outside the shell, r Rout . b. Find the electric field strength in the interior of the shell, r Rin. c. Find the electric field strength within the shell, Rin r Rout . d. Show that your solutions match at both the inner and outer boundaries.
ANSWER:a. Outside the shell, the electric field strength is given by Coulomb's law:
E(r) = k\frac{Q}{r^2}
where k= 8.99 x 10^9 N·m^2/C^2, Q is the total charge of the shell, and r is the distance of the point from the center of the shell. Thus:
E(Rout) = k