An infinite plane of charge has a uniform planar charge density and is located in the yz plane at x=0.A fixed point charge placed on the x-axis at x = + 1.0 m and the electric potential is a minimum on the x-axis at x=+0.31 m.What is the planar charge density on the plane?

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Quizplus · Accepted Answer

The electric potential due to an infinite plane of charge is given by:$$V = \frac{\sigma}{2\epsilon_0}x$$where $\sigma$ is the planar charge density, $\epsilon_0$ is the permittivity of free space, and $x$ is the distance from the plane.The electric potential is a minimum when the distance from the plane is a minimum. In this case, the distance from the plane is $x = +0.31$ m. Therefore, the planar charge density is:$$\sigma = \frac{2\epsilon_0V}{x} = \frac{2(8.85	imes10^{-12}	ext{ C}^2/	ext{Nm}^2)(100	ext{ V})}{0.31	ext{ m}} = +1.1	ext{ nC/m}^2$$

An Infinite Plane of Charge Has a Uniform Planar Charge