A 5 g piece of Styrofoam carries a net charge of - 0.5 µC and floats above the center of a very 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? The acceleration due to gravity is 9.8 m/s 2 and the permittivity of free space is 8.85419 * 10-12 C 2 / N/m2. Answer in units of µC/m2.

Charge per area = - 1.74u/cm^2

Explanation:

Mg=Fe ... eq1

The electric field due to the charge distribution on a large plastic surface is usually perpendicular between the surface

E = Chargeper area / (2Eo)

Where Eo is permittivity if free space

The force between a and the electric field will be:

Fe = qE = q * charge per area / (2Eo) ... eq2

Put eq1 into eq2

Mg = a * charge per area / (2*Eo)

Charge per area = mg * (2Eo) / a

Charge per area = (5/1000) * 9.8 * (2*8.85419*10^-12) / (-0.5*10^-6)

Charge per are = 1.74u/cm^2