When a shower is turned on in a closed bathroom, the splashing of the water on the bare tub can fill the room's air with negatively charged ions and produce an electric field in the air as great as 1000 N/C. Consider a bathroom with dimensions 3.5 m ✕ 2.5 m ✕ 2.0 m. Along the ceiling, floor, and four walls, approximate the electric field in the air as being directed perpendicular to the surface and as having a uniform magnitude of 550 N/C. Also, treat those surfaces as forming a closed Gaussian surface around the room's air.(a) What is the volume charge density ? C/m³
(b) What is the number of excess elementary charges e per cubic meter in the room's air? charges/m³

a) What is the volume charge density  = 1.15 x 10-8c/m3

b) What is the number of excess elementary charges e per cubic meter in the room's air = 7.18 x 10^10 charges/m3

Explanation:

The Concept of Gauss law was applied, the gauss law which relates the electric fields at points on a closed gaussian surface and the net charge enclosed by the surface. The gaussian surface most times are always a sphere, cylinder or in some other symmetrical form, and it must always be a closed surface.

The law was named after the german mathematician and physicist Carl Friedrich Gauss. It was a more elaborate explanation of Coulomb's law.

The steps and necessary susbstitution is as shown in the attached file.

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