A long charged cylinder of linear charged density l is surroundedby a hollow co-axial conducting cylinder. What is the electric field inthe space between the two cylinders?
Given: The linear charged density of a long charged cylinder is λ .
Electric flux through the Gaussian surface is given as,
ϕ = E ( 2 π d ) L (1)
Where, the distance of a point from the common axis of the cylinders is d , the electric field between the two cylinders is E and the length of the cylinder is L .
The electric flux is given as,
ϕ = q ε 0 (2)
Where, the total charge on the cylinder is q and the permittivity of free space is ε 0 .
From equation (1) and (2) it can be written as,
E ( 2 π d ) L = q ε 0 E ( 2 π d ) L = λ L ε 0 E = λ 2 π ε 0 d
Thus, the electric field in the space between the two cylinders is λ 2 π ε 0 d .
Given: The linear charged density of a long charged cylinder is
Electric flux through the Gaussian surface is given as,
Where, the distance of a point from the common axis of the cylinders is
The electric flux is given as,
Where, the total charge on the cylinder is
From equation (1) and (2) it can be written as,
Thus, the electric field in the space between the two cylinders is
