Que:

In the circumstances of charge distributed on a line segment what do we mean by the expression linear charge density λ(x)?

Note that λ(x) is to be study lambda of x meaning that the linear charge density is a function of x where x is the position along the line segment in question.

Ans:

Any definition that begins out with the amount of charge has got to be wrong. Linear charge density is absolutely not an amount of charge. Dividing the whole charge on the line segment by the length of the line segment does give the average charge density but the average charge density is of about as much use in determining the electric potential as the average speed of a motorist who has been pulled over for doing 80 mph in a 40 mph zone is to the motorist. However officer I left my house at noon and it's 1 pm now. I am now 40 miles from my house consequently clearly my average speed is 40 mph doesn't cut it with the officer and treating the average charge density as if it were the actual charge density does not cut it in physics.

The linear charge density is certainly a charge packing index a value (with units of course) which indicates how closely packed the charges are.