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What is the electric flux (∫ E · d a) 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 ?
- HQ/ε0
- HQ/4ε0
- Hε0/4Q
- 4H/Qε0
Correct answer: HQ/4ε0
Solution
The electric flux through the quarter-cylinder is determined by the symmetry of the electric field produced by the infinitely long line charge, which leads to a quarter of the total flux that would pass through a full cylinder. Thus, the correct expression for the flux is a quarter of the total flux, resulting in HQ/4ε0.
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