Question

The electric field intensity due to a infinite wire having linear charge density LAMDA at a perpendicular distance r from wire is


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Answer 1

Answer:

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Answer 2

The electric field intensity due to an infinite wire having linear charge density LAMDA at a perpendicular distance r from the infinite wire is:

(A) λ / 2πε₀r

- Let us consider a Gaussian surface (cylinder) of radius r and length l around the wire.  

- The amount of charge enclosed by this cylinder:

q  = (λ × l)

- The surface area of the cylinder:

A = 2πrl

- Then according to the Gauss's Law of electrostatics:

∫  E.dA  = q /ε₀  

- From symmetry, we can easily deduce that the electric field will only be along the radial direction.

⇒ E × A = q /ε₀

⇒ E × 2πrl = (  λ × l)/ε₀

⇒ E = λ / 2πε₀r