Question

A 2.0 m × 4.0 m horizontal plastic sheet has a charge of −10 μC , uniformly distributed. A tiny 4.0 μg plastic sphere is suspended motionless just above the center of the sheet. What is the charge on the sphere?

Answer 1

Answer:

Explanation:

Given

Dimension of Plastic sheet is $2\times 4\ m^2$

Charge on sheet $Q=-10\ \mu C$

Charge density $\sigma =\frac{q}{A}$

$\sigma =\frac{-10\times 10^{-6}}{8}=1.25\times 10^{-6}\ C/m^2$

Sphere has mass of  $m=4\ \mug$

If sphere is suspended motionless then its weight is balanced by repulsion force

Repulsive force $F_r=qE$

where E=Electric field due to sheet

$E=\frac{q}{2\epsilon _0}$

$E=\frac{-10\times 10^{-6}}{2\times 8.85\times 10^{-12}}$

$E=5.647\times 10^{5}\ N/C$

$F_r=q\times 5.647\times 10^{5}$

$F_r=mg$

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

$q=\frac{4\times 10^{-6}\times 9.8}{5.647\times 10^{5}}$

$q=6.9417\times 10^{-11}\ C$