3. A coaxial cable consists of a copper wire, radius a, surrounded by a concentric copper...

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3. A coaxial cable consists of a copper wire, radius a, surrounded by a concentric copper tube of inner radius b and thickness c-b. The area between these two conductors is filled with a dielectric with permittivity € (as shown below). The inner and outer conductors are held at potentials V₁ and V, respectively. Find: (a) Ē, Ď and P everywhere Hint: Start by solving Laplace's equation in cylindrical coordinates (s, o, z) to show that within the dielectric the potential takes the form V(s) = V₁ + (Vb - Va) € (b) The bound surface and volume charge density everywhere, and the net bound charge (c) The free charge on the inner and outer conductors, and the capacitance. a In(s/a) In(b/a) C 3. A coaxial cable consists of a copper wire, radius a, surrounded by a concentric copper tube of inner radius b and thickness c-b. The area between these two conductors is filled with a dielectric with permittivity € (as shown below). The inner and outer conductors are held at potentials V₁ and V, respectively. Find: (a) Ē, Ď and P everywhere Hint: Start by solving Laplace's equation in cylindrical coordinates (s, o, z) to show that within the dielectric the potential takes the form V(s) = V₁ + (Vb - Va) € (b) The bound surface and volume charge density everywhere, and the net bound charge (c) The free charge on the inner and outer conductors, and the capacitance. a In(s/a) In(b/a) C