# 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

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

×