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Question
In case of an infinite line charge, how does intensity of electric field at a point change, if at all, when.
- charge on it is doubled?
- distance of the point is halved?
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Solution
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.
- 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. - 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.
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