Ncert Exercises & Solutions

A long charged cylinder has a linear charge density λ and is surrounded by a hollow coaxial conducting cylinder. What is the electric field in the space between the two cylinders at a radial distance r from the axis of the inner cylinder?
1. \(E=\dfrac{\lambda}{2\pi \epsilon_0 r^2},\) radially outward
2. \(E=\dfrac{\lambda}{2\pi \epsilon_0 r},\) radially outward
3. \(E=\dfrac{\lambda}{4\pi \epsilon_0 r},\) radially outward
4. \(E=0\)

The charge density of the long charged cylinder of length L and radius r is Another cylinder of the same length surrounds the previous cylinder. The radius of this cylinder is R.

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

The electric flux through the Gaussian surface is given by Gauss's theorem as,

ϕ = E (2 πd) 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 (2 πdL) = \frac{q}{ε_{0}}

Where, q Charge on the inner sphere Of the outer cylinder

ε_{0}

= permittivity of free space

\begin{array}{l} E (2 πdL) = \frac{λL}{ϵ_{0}} \\ E = \frac{λ}{2 {πϵ}_{0} d} \end{array}

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

\frac{λ}{2 {πϵ}_{0} d}

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