A thin straight infinitely long conducting wire having charge density λ is enclosed by a cylindrical surface of radius r and length l, its axis coinciding with the length of the wire. Find the expression for the electric flux through the surface of the cylinder.
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Ф=∫E.ds cosθ
here θ=0°
since its axis coincides with the length of the wire
⇒Ф=E∫ds
Ф=E(2πrl) is the electric flux through the surface of the cylinder ∵∫ds=A (surface area of the cylinder)
[by gauss law Ф=q/ε,where q is the net charge enclosed by the cylindrical surface and ε permittivity of the medium in which the wire is in]
so,q/ε=E2πrl
⇒E=1/2πε.q/rl (here q/l=λ linear charge density)
∴E=1/2πε.λ/r
here θ=0°
since its axis coincides with the length of the wire
⇒Ф=E∫ds
Ф=E(2πrl) is the electric flux through the surface of the cylinder ∵∫ds=A (surface area of the cylinder)
[by gauss law Ф=q/ε,where q is the net charge enclosed by the cylindrical surface and ε permittivity of the medium in which the wire is in]
so,q/ε=E2πrl
⇒E=1/2πε.q/rl (here q/l=λ linear charge density)
∴E=1/2πε.λ/r
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