A very long hollow cylindrical pipe with an inner radius of a and an outer radius of b is lined up with the z-axis. This pipe is made of a material that carries a volumetric charge density of p, = k/p in the region a spsb,where k is a positive constant. Assume that the permittivity of the pipe's material is e. a. Determine an expression for the electric field everywhere in the region p < a. b. Determine an expression for the electric field in the region a
A very long hollow cylindrical pipe with an inner radius of a and an outer radius of b is lined up with the z-axis. This pipe is made of a material that carries a volumetric charge density of p, = k/p in the region a spsb,where k is a positive constant. Assume that the permittivity of the pipe's material is e. a. Determine an expression for the electric field everywhere in the region p < a. b. Determine an expression for the electric field in the region a
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Transcribed Image Text:A very long hollow cylindrical pipe with an inner radius of a and an outer radius of b is lined up
with the z-axis. This pipe is made of a material that carries a volumetric charge density of p, =
k/p in the region a sps b, where k is a positive constant. Assume that the permittivity of the
pipe's material is e.
a. Determine an expression for the electric field everywhere in the region p < a.
b. Determine an expression for the electric field in the region a < p < b.
c. Use the result in part (b) to show that the potential difference between a point at p = b
and a point at p = a is AV = - [(a – b) – a In (E).
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