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An infinitely long line, with uniform positive charge density, lies along the z-axis. In cylindrical coordinates (r, ϕ, z), at any point \(\vec P\) not on the z-axis, the direction of the electric field is 


1. r̂ 
2. ϕ̂
3. ẑ 
4. \(\frac{(\hat r+ \hat z)}{\sqrt{2}}\)

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Correct Answer - Option 1 : r̂ 

Concept:

Let positive charge density is ρl

Given that charge lies along the z-axis, and we have calculated the electric field at any point p which lies in the x-y axis, not on the z-axis.

So the expression of the electric field is given by 

E = (ρ× âr ) /(2π × ϵ × r) 

Where r is the unit vector in direction of r  

From the above expression, it is clearly shown that it has the direction in r.

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