Question

Using Gauss’s law, derive expression for intensity of electric field at any point near the infinitely long straight uniformly charged wire.

Answer 1

electric field due to infinitely long straight wire at a distance r from it is given by, λ/2πε0r.

Let an infinitely long straight wire of linear charge density λ. a cylindrical gaussian surface is drawn as shown in figure.

charge inside gaussian surface, Q_in = λdl

now from Gauss law,

electric flux, Φ = Q_in/ε0

⇒electric field . area of gaussian surface = λdl/ε0

⇒electric field . 2πr dl = λ dl/ε0

⇒electric field = λ/2πε0r

hence, electric field due to infinitely long straight wire at a distance r from it is given by, λ/2πε0r

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Answer 2

$\huge\bold\purple{Answer:-}$

Gauss Theorem : The net outward electric flux through a closed surface is equal to 1/ε0 times the net charge enclosed within the surface i.e., ... Thus, the electric field strength due to a line charge is inversely proportional