Question

the liners charge density with long charge cylinders in hellow coaxial conductor slender by surrounded is the two cylinder of the middle of the space in the electric field so that?​

Answer 1

Explanation:

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

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

Let E be the electric field produced in the space between the two cylinders.

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

ϕ=E(2πd)L

Where, d= Distance of a point from the common axis of the cylinders

Let q be the total charge on the cylinder.

It can be written as

$∴ϕ=E(2πdL)=∈0q</p><p>$

Where,

q= Charge on the inner sphere of the outer cylinder

$∈0</p><p>$

= Permittivity of free space

$E(2πdL)=∈0λL</p><p>$

$E=2π∈0dλ</p><p>$

Therefore, the electric field in the space between the two cylinders is

$2π∈0dλ.$