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A long charged cylinder of linear charge density lambda is surrounded by a hollow co-axial conducting cylinder. What is the electric field in the space between the two cylinders ?

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Answer Text

Solution :
Charge density of the long charged cylinder of length L and radius r is `lambda`. Another cylinder of same length surrounding the previous cylinder. The radius of the cylinder is R. <br> Let E be the E.F produced in the space between the two cylinders. electric flux. through the gaussian surface is given by gauss's theoram as, <br> `phi=E(2pid) L` <br> Where, d=distance of a point from the common axis of the cylinders let q be the total charge on the cylinder. <br>it can be written as <br> `:. phi=E=(2pidL) =q/(in_(0))` <br> where, q=charge on the inner sphere of the outer cylinder <br> `in_(0)`=permitivity of free space <br> `E(2pidL)=(lambdaL)/(in_(0))` <br> `E=(lambda)/(2piin_(0)d)` <br> Therefore, the electric field in the space between the two cylinders is `(lambda)/(2piin_(0)d)`

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