A thin straight infinitely long conducting wire having charge densi...

Question

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.

Accepted Answer

Given:
• Linear charge density = λ
• Length of cylinder = l
• Radius of cylinder = r
• Wire passes through the axis of cylinder

Step 1: Calculate enclosed charge
q_enclosed = (charge per unit length) × (length)
q_enclosed = λl

Step 2: Apply Gauss's Law
φ = q_enclosed/ε₀

Step 3: Substitute
φ = λl/ε₀

Note on flux distribution:
• Flux through curved surface = λl/ε₀ (E perpendicular to surface)
• Flux through flat ends = 0 (E parallel to surface)
• Total flux = λl/ε₀

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