Induced Charge on a Grounded Conducting Cylinder

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A long, grounded conducting cylinder of length $L$ and radius $R$ is oriented with its axis perpendicular to a uniform electric field $E$ . What is the total induced charge on the cylinder’s surface?

$0$

$\pi\varepsilon_0 E R^2$

$2\pi\varepsilon_0 E R L$

$4\pi\varepsilon_0 E R^2$

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