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Question -

A long charged cylinder of linear chargeddensity λ is surrounded by a hollow co-axial conducting cylinder. What is theelectric field in the space between the two cylinders?



Answer -

Charge density of the long charged cylinderof length L and radius r is λ.

Another cylinder of same length surroundsthe pervious cylinder. The radius of this cylinder is R.

Let E be the electricfield produced in the space between the two cylinders.

Electric flux through the Gaussian surface is given byGauss’s theorem as,

Where, = Distance of apoint from the common axis of the cylinders

Let q be the total chargeon the cylinder.

It can be written as

Where,

q =Charge on the inner sphere of the outer cylinder

0 = Permittivityof free space

Therefore, the electricfield in the space between the two cylinders is 

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