How Do You Calculate the Surface Charge Density on a TV Screen?

AI Thread Summary
To calculate the surface charge density on a TV screen, the force acting on a dust mote is determined using F = ma, resulting in 5E-8 N. The electric field (E) is then calculated by dividing the force by the charge, yielding 50 N/C. The surface charge density (σ) is found using the formula σ = 2*E*εo, which gives a result of 8.85E-10 C/m2. It's important to ensure proper unit conversions, particularly from micrograms to kilograms. This calculation illustrates the relationship between charge density and the forces acting on small particles near charged surfaces.
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Homework Statement



  1. You've probably noticed that TV screens and computer monitors have an annoying tendency to accumulate dust. Wanting to understand this better, you decide to model the situation as follows: you assume a small mote of dust might have an excess charge of 1 nC and a mass of 5 μg. It floats near the surface of a television screen, accelerating toward the screen at a rate of 10 mm/s^2. You would like to know the surface density of the charge on the screen.

Homework Equations


F = ma
E = F / q
σ = 2*E*εo

The Attempt at a Solution


I keep getting the problem wrong and would like someone to check over my work and tell me what I'm doing wrong.

F = ma = 5E-6kg * 0.010m/s2 = 5E-8 N

E = F / q = 5E-8N / 1E-9C = 50 N/C

σ = 2*E*εo = 2 * 50N/C * 8.85E-12C2/N·m2 = 8.85E-10 C/m2
 
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Check the conversion from μg to kg.
 

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