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Surface Charge Density of shower

  1. Sep 17, 2010 #1
    1. The problem statement, all variables and given/known data

    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 2.3 m x 3.6 m x 1.6 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 647 N/C. Also, treat those surfaces as forming a closed Gaussian surface around the room's air. What are (a) the volume charge density ρ and (b) the number of excess elementary charges e per cubic meter in the room's air?

    2. Relevant equations
    E dot DA = q
    q = [tex]\phi\epsilon[/tex]

    3. The attempt at a solution

    for part a
    I took the area of each face and multiplied it by the net E feild forces
    (-647 - 647)
    and i got that right
    apparently density can be negative?
    mostly what i don't understand is how to go about solving part b
    I have no idea what it's asking...
  2. jcsd
  3. Sep 17, 2010 #2


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    Homework Helper
    Gold Member

    Yes, when the net charge (within the volume) is negative.
    elementary charge, e = 1.60217646 × 10-19 Coulombs (use positive or negative as appropriate, and significant figures as appropriate for your coursework.)
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