An infinite charged wire with charge per unit length lambda lies along the central axis of a cylindrical surface of radius r and

Question

Mkey [24]

2 years ago

14

An infinite charged wire with charge per unit length lambda lies along the central axis of a cylindrical surface of radius r and

length . What is the flux through the surface due to the electric field of the charged wire?

Physics

1 answer:

serg [7] · Answer 1 · 2023-10-19T01:49:36+03:00

<h2>The flux through the infinite charged wire along the central axis of a cylindrical surface of radius r and length l is ∅E = E x 2πrl </h2>

Explanation:

let us consider a thin infinitely long straight wire having a uniform charge density λ Cm⁻¹.To determine the field at a distance r from the line charge , we have cylindrical gaussian surface of radius r, length l,and with its axis along the line charge. it has curved surface S₁ , and flat circular ends S₂ and S₃. Obviously, dS₁//E, dS₂ ⊥E , and dS₃ ⊥ E , so, only the curved surface contributes towards the total flux.

∅E = ∫ E.dS = ∫E.dS₁ +∫E.dS₂ +∫E.dS₃

= ∫EdS₁ cos0⁰ +∫EdS₂ cos 90⁰ +∫Eds₃ cos 90⁰

= E∫ds₁₁ +0+0

= E x area of curved surface

∅E = E x 2πrl