Question

A 17 2-g biece of Styrafoam carries a net charge of 0 658 C and is suspended in equlibriam above the coester of a large, hortonta shee of plasic tht has a uniform charge density on its surface What unit ares on the plastic sheet?

Answer 1

When the styrofoam is suspended, the gravitational force is balanced by the Electric field produced by the sheet below, Hence we can write,

$F_g = F_E \Rightarrow mg = qE$

$\Rightarrow E = \frac{mg}{q}$

$\Rightarrow E = \frac{(17.2 \times 10^{-3})(9.81)}{0.658 \times 10^{-6}} = 2.56 \times 10^5 \, N/C$

The electric field produced by the sheet is given by,

$E = \frac{\sigma}{2 \epsilon_0}$

Substituting values we get,

$\Rightarrow \frac{\sigma}{2 \epsilon_0} = 2.56 \times 10^5 \, N/C$

$\Rightarrow \sigma = 4.53 \times 10^{-6} \, C/m^2 = 4.53 \, \mu C/m^2$