There is a very thin straight pipe of a large length. A transparent insulating material is used to make this pipe. The inner radius of pipe is r and the outer radius is R. Both R and are very small and the difference between them is very less. The pipe is fixed in a vertical orientation. The upper end of the pipe is open and its lower end is closed. There is a large number of small insulating spheres of radius r each carrying charge Q. These small spheres are inserted from the upper end of the pipe one after another and pushed down further so that entire pipe is filled with closely spaced insulating charged sphere. Electric field due to this system is observed for points outside the pipe and towards the midpoint of large vertical length of pipe.
If we compare the given system with a line charge then what will be the equivalent value of linear charge density.

Options

A. Q/r
B. `Q//2pir`
C. Q/2r
D. None

Answer

C

Explanation

The system is equivalent to line charge of a large length. Insulating charged spheres are closely spaced so charge Q can be taken to be distributed in length 2r on an average basis. Linear charge density is charge per unit length. Thus, the equivalent linear charge density can be written as follows:
`lambda=Q/(2r)`