Electric Flux Problem: Finding Charge per Unit Area on a Charged Plastic Sheet

[MJay82]

Homework Statement

A 15.2-g piece of Styrofoam carries a net charge of -0.702 µC and is suspended in equilibrium above the center of a large, horizontal sheet of plastic that has a uniform charge density on its surface. What is the charge per unit area on the plastic sheet?

Homework Equations

F=ma (sum of the forces in the Y direction = 0 )
Φ = k/ε0

The Attempt at a Solution

I'm really not sure here. Usually if I don't have an idea of what I'm doing, I'll look at the way the units interact.

Here something like
Surface charge density = Weight/Φ gives me the correct units, but not the right answer.

 

[anathema]

Hello there,

Thank you for your post. Let me see if I can help you out with this problem.

First, let's define some variables:

Q = net charge on the Styrofoam piece
m = mass of the Styrofoam piece
g = acceleration due to gravity
d = distance between the Styrofoam piece and the center of the plastic sheet
σ = charge per unit area on the plastic sheet

Now, we can use the equation F=ma to set up an equation for the forces acting on the Styrofoam piece:

F = Qσ - mg = 0

Since the Styrofoam piece is in equilibrium, the sum of the forces must be equal to zero. Solving for σ, we get:

σ = mg/Q

We can now plug in the given values and solve for σ:

σ = (15.2 g)(9.8 m/s^2)/(-0.702 µC) = -219.2 µC/m^2

This tells us that the charge per unit area on the plastic sheet is -219.2 µC/m^2. This means that the plastic sheet has an excess of negative charge, since the Styrofoam piece has a negative charge and is being repelled by the plastic sheet.

I hope this helps you with your problem. Let me know if you have any further questions.