Question

In case of an infinite line charge, how does intensity of electric field at a point change, if at all, when.

1. charge on it is doubled?
2. distance of the point is halved?

Answer 1

The intensity of the electric field E at a point located at a distance r from the line charge is `E = λ/(2π∈_0r)` where, λ is the charge per unit length.

1. The charge on it is doubled.
   Given λ = 2λ
   ∴ E' = `λ/(2π∈_0r)`
   New electric field intensity
   E' = `(2λ)/(2π∈_0r)`
   = `2⋅ λ/(2π∈_0r)`
   = 2E
   Thus, the intensity of the electric field is doubled.
2. The distance of the point is halved:
   Given, r' = `r/2`
   ∴ E' = `λ/(2π∈_0r"'")`
   New electric field intensity
   E' = `λ/(2π∈_0(r/2))`
   = `2⋅λ/(2π∈_0r)`
   = 2E
   Hence, the intensity of the electric field is also doubled in this case.