Obtain the expression of electric field at any point by continuous distribution of charge on a line.

Explanation

Suppose, line is divided into smaller elements of dl length and `vecr` is the position vector of any smaller element and its linear charge density is `lambda` and its charge is `lambdadl`.

Suppose a point P (inside or outside) whose, position vector is `vecR`.
P is at `r.` distance from Al element and unit vector is `vecr`.
Electric field at P due to `lambdaDeltal`
`vec(DeltaE) = (klambda Deltal)/(r.)^(2).hatr`
Total electric field at P by superposition principle.
`vecE = sum_(Deltal) (klambdaDeltal)/(r.)^(2).r`
By integration method.
`vecE = int_(l) (klambdadl)/(r.)^(2).hatr`