Question

Three very large parallel non-conducting planes (infinte planes) have surface charge densities of ?, −? and – 3? (? > 0). Planes are distance ? apart from each other. The origin of the coordinate system was set on the first plane as shown in the figure. Planes are perpendicular to z axis. Point A is 1/2 ? away from the origin while point B and P are 2 ? and 4 ? away from the origin respectively. a) Use Gauss’s law, find the electric field due to a single infinite plane with a constant surface charge density ? . b) Calculate electric fields due to three planes at points A, B and P. c) Find the net force exerted by three planes on a point charge Q located at B. What is the force on a point charge Q located at A? d) A lab instructor accidently added / subtracted some charges from the first plane (leftmost plane). Therefore, we do not know the surface charge density of the frist plane. However, it is found that the electric field at point B is zero. The surface charge density of the third plane is measured to be −3 ?/?2 . What is the surface charge density of the first plane?

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