Charged Ring Over An Infinite Grounded Plane

A thin ring of radius R\displaystyle R is charged with a charge q\displaystyle q. It is then placed over an infinitely large grounded conducting plane at a height h\displaystyle h, as shown in the figure above.

Find the magnitude of the surface charge density σ\displaystyle \sigma (in C/m2^2) of the induced charge at the point on the plane which is exactly below the ring's center.

Details and Assumptions

\bullet q=2 μC\displaystyle q = 2\ \mu\text{C}
\bullet R=10 cm\displaystyle R = 10\text{ cm}
\bullet h=15 cm\displaystyle h = 15\text{ cm}

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