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