A small section of an infinitely long charge distribution is shown at right. A l

Question

A small section of an infinitely long charge distribution is shown at right. A line charge of linear charge density ?(line) = 1.5 nC/m is at the center. It is surrounded by an inner cylinder is made from insulating material, which has a radius of 1.5 cm, and has a volume charge density given by ?(inner). The outer cylindrical shell is made of a conducting material, of inner radius 5 cm and outer radius 6 cm. The outer cylindrical shell has an overall charge per unit length given by ?(outer) = -2.5 nC/m.

Suppose the inner cylinder had a uniform charge density of ?(inner) = 2.8

Explanation / Answer

ets take a small length element dx, q is the total charge, l is total length, a is distance from nearer end. dq=(q/l)dx dE=dq/{4p?o(a+x)^2 } substitute for dq: dE = qdx / {4p?ol(a+x)^2} E = q / 4p?ol?_0^l¦(a+x) ^(-2)dx (integrating giving proper limits upper limit=l, lower limit= 0) E=q / {4p?o(a+l)} solve for q=3.5nC/m*5m=17.5nC, l = 5m, a = 6 - 5 = 1m e) use columb's law directly, taking q=17.5nC, r= 270m,

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