GATE EC 2019 Set 1 — Question 21
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Electromagnetics → Maxwell's Equations → Differential & Integral Forms
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Question
What is the electric flux () through a quarter-cylinder of height H (as shown in the figure) due to an infinitely long line charge along the axis of the cylinder with a charge density of Q?
Correct answer
(B) (HQ)/(4ε₀)
Solution
Treat as the line-charge density (C/m). The field of an infinite line charge is radial: .
- Curved face (a quarter of the full cylinder, from 0 to , at radius ):
- Flat rectangular faces: they contain the axis, so lies in their plane and gives zero flux.
- Top and bottom faces: , so zero flux.
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