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Class 12 › Physics › Electric Charge and Field
CBSE2024Class Class 12 · Physics3 Marks · Short✅ Verified
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.
✅ Answer & Solution
<b>Given:</b><br>• Linear charge density = λ<br>• Length of cylinder = l<br>• Radius of cylinder = r<br>• Wire passes through the axis of cylinder<br><br><b>Step 1: Calculate enclosed charge</b><br>q<sub>enclosed</sub> = (charge per unit length) × (length)<br>q<sub>enclosed</sub> = <b>λl</b><br><br><b>Step 2: Apply Gauss's Law</b><br>φ = q<sub>enclosed</sub>/ε<sub>0</sub><br><br><b>Step 3: Substitute</b><br><b>φ = λl/ε<sub>0</sub></b><br><br><b>Note on flux distribution:</b><br>• Flux through <b>curved surface</b> = λl/ε<sub>0</sub> (E perpendicular to surface)<br>• Flux through <b>flat ends</b> = 0 (E parallel to surface)<br>• Total flux = λl/ε<sub>0</sub>
