Q.

The electric field at distance ‘r’ from infinite line of charge (having linear charge density λ ) is __

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a

λπε0r

b

λ2πε0r

c

λ4πε0r

d

λε0r

answer is A.

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Detailed Solution

On considering a Gaussian surface (cylinder in this case) of radius r and length l. 
Then according to the Gauss's Law of electrostatics:

E·dA= qenclosed ϵ0

From the symmetry of the surface, we can easily say that the electric field would only be along the radial direction. And the amount of charge enclosed by this cylinder is charge enclosed =λ×l and the surface area of the cylinder A=2πrl. 

E×2πrl=λlϵ0

E=12πϵ0λr

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