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What is the electric flux $\left(\int \vec{E}.d \hat{a}\right)$ 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 $Q?$

  1. $\frac{HQ}{\varepsilon_{0}}$
  2. $\frac{HQ}{4\varepsilon_{0}}$
  3. $\frac{H\varepsilon_{0}}{4Q}$
  4. $\frac{4H}{Q\varepsilon_{0}}$ 
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