Electric Field Intensity Outside an Infinitely Long Charged Cylindrical Conductor

The electric field intensity at a point outside an infinitely long charged cylindrical conductor can be derived using Gauss's law. Gauss's law states that the electric flux through a closed surface is proportional to the enclosed charge.

Deriving the Expression

- Consider a cylindrical surface of length L and radius r, with one end at the point where we want to find the electric field intensity.
- The electric field lines are perpendicular to the surface of the cylinder, and their magnitude is constant along the surface as the cylinder is infinitely long.
- The electric flux through the surface can be calculated as the product of the electric field intensity and the area of the cylindrical surface.
- As the cylinder is infinitely long, the electric flux through the curved surface of the cylinder is zero.
- The only contribution to the electric flux comes from the two circular ends of the cylinder.
- The electric field lines are radial at the ends of the cylinder, and the electric field intensity is constant along the circular ends.
- The electric flux through each end of the cylinder is proportional to the enclosed charge within the cylinder.
- The enclosed charge within the cylinder is the product of the charge density and the volume of the cylinder.
- The volume of the cylinder is given by the product of the length L and the area of the circular cross-section of the cylinder.
- Using Gauss's law, we can write the expression for the electric field intensity as E = λ/(2πεr), where λ is the linear charge density of the cylinder, ε is the permittivity of the medium, and r is the distance from the axis of the cylinder.

In conclusion, the electric field intensity at a point outside an infinitely long charged cylindrical conductor is given by the expression E = λ/(2πεr), where λ is the linear charge density of the cylinder, ε is the permittivity of the medium, and r is the distance from the axis of the cylinder.