Charged Ring Over An Infinite Grounded Plane

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

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

Details and Assumptions

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


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