Given the expression for electric field intensity at a point due to a thin infinitely long straight wire. Give the meaning the of symbols used.

Explanation

Electric field intensity due to a thin long wire : A line charge is in the form of a thin charged rod with unform linear charge density `lambda` (charge per unit length),
To determine the electric field intensity `vecE` at any point P at a perpendicular distance r from the rod let a right circular closed cylinder of radius r and lenght l with the infinitely long line of charge as its axis (as shown in figure). The magnitude of `vecE` at every point on the curved surface of the cylinser is the same as all such points are at the same distance from the line charge . Also `vecE` and unit vector `hatn` normal to curved surface are in the same direction so `theta=0^(@)`.
`therefore` Contribution of curved surface of cylinder towards electric flux ,
`oint_(s)vecE*vecds=ointvecE*hatnds`
`=Eoint_(s)ds=E(2pirl)` where `(2ppiel)` is area of the curved surface of the cylinder.
On the ends of cylinder , the angle between electric field `veceandhatn` is `90^(@)` . So it will not contribute to electric flux on cylinder.
`rArrointvecE*vecds=Exx2pirl`
Charge enclosed in the cylinder
i.e = linear charge density `xx` lenght
`q=lambdal`
According to Gauss.s theorem `ointvecE*vecds=(q)/(epsilon_(0))`
`rArr(2pirl)xxE=(lambdal)/(epsilon_(0))`
`E=(lambdal)/(2piepsilon_(0)rl)`
`thereforeEprop(l)/(r)`
(As `(lambda)/(2piepsilon_(0)r)=`constant)