An infinitely long cylinder in free space is concentric with the z-axisand has radius a. The net charge density p in this cylinder is given incylindrical coordinates by,1a² +r²where A is a constant.(a) Show that the total charge per unit length, λ in the cylinder isλ = πA ln 2.p(r) = A-Hint: you may find the following integral useful.12Jfor r a) and inside thecylinder (r< a).(d) The cylinder is composed of a material in which the polarisation Pis given byP = P₁² in (1 +5²) e₁₁er,rwhere Po is a constant.Determine the bound charge density pb in the cylinder. Hence, orotherwise, determine a relation between A and Po such that thefree charge density of in the cylinder vanishes.

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An infinitely long cylinder in free space is concentric with the z-axis and has radius a. The net charge density p in this cylinder is given in cylindrical coordinates by, 1 a² + ² where A is a constant. (a) Show that the total charge per unit length, À in the cylinder is p(r) = A for r