Question

A 27g piece of Styrofoam carries a net charge of -0.75 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?

I'm having trouble visualizing the basic concept..like for this one i don't how to draw the picture first...

Answer 1

The force of repulsion between the electric field created due to horizontal sheet of plastic having surface charge density `sigma` and charge on the styrofoam piece is balancing the weight of the styrofoam piece placed at `i` in the figure above.

`mg = F_e` ......(1)

Electric field due to charge distribution on large plastic sheet, considered infinite, is perpendicular to the surface

`E= sigma/(2epsilon_0)`
where `epsilon_0` is the permittivity of free space.

Force between the charge `q` and the electric field

`F_e=qE=qsigma/(2epsilon_0)`

Using (1) and solving for `sigma`

`mg = qsigma/(2epsilon_0)`
`=> sigma=mgxx (2epsilon_0)/q` .......(2)

Inserting various values in SI units in (2)
`σ= 27/1000xx9.81xx(2xx8.85 xx 10^-12) / (-0.75 xx 10^-6)`
`= -6.25 μC m^-2`, rounded to two decimal places.