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GATE 2019 EC – Question 21

Electromagnetics · Maxwell's Equations · 1 mark · Multiple choice

What is the electric flux $\left(\int\vec E\cdot d\vec a\right)$ 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 $Q$?

Diagram for GATE 2019 EC question 21
  1. $\dfrac{HQ}{\varepsilon_0}$
  2. $\dfrac{HQ}{4\varepsilon_0}$
  3. $\dfrac{H\varepsilon_0}{4Q}$
  4. $\dfrac{4H}{Q\varepsilon_0}$

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Show answer and explanation

Correct answer: (B) $\dfrac{HQ}{4\varepsilon_0}$

Explanation

For the whole cylinder of height $H$, Gauss's law gives $\frac{QH}{\varepsilon_0}$. By symmetry a quarter of the cylinder carries a quarter of the flux, $\frac{HQ}{4\varepsilon_0}$.