A line charge lambda is located a distance d from the axis of very long conducti

Question

A line charge lambda is located a distance d from the axis of very long conducting cylinder and is parallel to the axis. Using an image line charge-lambda at an appropriate (a = R^2/d) place inside the cylindrical region solve the electrostatic problem. What is the electrostatic potential due to a line charge in free space? What is the electrostatic potential phi(r, phi) outside the conductivity cylinder with the potential in b) is constant on the surface of the cylinder. Find the surface charge density on the cylinder What is the force per unit area on the surface of the cylinder?

Explanation / Answer

a)

Given length is 4 units

Linear charge density is =Q/4

Small element of charge is dQ=dy

dV in terms of linear charge density is dV=dQ/40r

=dy/40x^2+y^2

on integrating from 0 to 4 units we will get the

ElectroStatic Potential as

V=dy/40*[0-4]dy/x^2+y^2

=dy/40ln(((16+x^2)+2)/((16+x^2)-2))

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