Capacitance between infinite plane and cylinder

Please provide a solution for this problem. Thank you!

@Damir @Alisher @Miras

If the conducting plane is grounded then its potential \varphi=0. You should use the method of images and imagine that there’s another cylinder on the other side of the grounded plane. Then use the formula \varphi_2-\varphi_1=-\int\limits_{1}^{2}\vec E(\vec r')\vec {dr'} to find the potential difference between the cylinder and its image. You can assume that the capacitance per unit length is C=\frac{\lambda }{V}

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Also there is a part B.1 from T1 of the APhO 2019 which is very similar to this problem.

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Oh I see, let me have a look!

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