When a shower is turned on in a closed bathroom the splashin

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 treat at 1000.0 N/C. Consider a bathroom with dimensions 25 m Times 3.0 m Times 2.0 m. Along the ceiling floor, and four walls, approximate the electric field in the air at being directed perpendicular to the surface and as having a uniform magnitude of 750.0 N/C. Also, treat those surfaces at forming a closed Gaussian surface around the room\'s air. [Place your diagram above this text] What is the volume charge density rho ?

Solution

Here,

electric field , E = 750 N/C

let the charge volume density is p

Using gauss law

p * V/epsilon_0 = flux through the surface

p * 2.5 * 3 * 2/(8.854 *10^-12) = 750 * (2 * 2.5 * 3 + 2 * 2 * 2.5 + 2 * 2 * 3)

solving for p

p = 1.64 *10^-8 C/m^3

the volume density of the charge inside is 1.64 *10^-8 C/m^3