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A wire containing a charge of λ Coulombs per unit length is embedded along the axis...

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Physics

A wire containing a charge of λ Coulombs per unit length isembedded along the axis of a cylinder of dielectric material. Thereis no free charge inside the dielectric. The composition of thedielectric is non-uniform, such that its permittivity is a functionof the distance from the central axis, i.e. ε = ε(r).

(a) Find the displacement field, D as a function of distancefrom the central axis of the wire, r.

(b) if the electric field strength, E, is independent of r,determine the form of ε(r).

(c) Find an expression for the electrostatic potential as afunction of r.

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