Question

A speck of dust has a mass of 1.0 x 10-18 kg and carries a charge equal to that of one electron.

Near to the Earth's surface it experiences a uniform downward electric field of strength

100 N C-1 and a uniform gravitational field of strength 9.8 N kg-1.

Draw a free-body force diagram for the speck of dust. Label the forces clearly.

Calculate the magnitude and direction of the resultant force on the speck of dust.

Answer 1

Given:

$m=1.0\times 10^{-18}\:\rm kg$

$q=1.6\times 10^{-19}\:\rm C$

$E=100\:\rm N/C$

$g=9.8\:\rm N/kg$

The resultant force

$$F_{\rm net}=mg-qE\\ =1.0\times 10^{-18}\:{\rm kg*9.8\:N/kg}\\-1.6\times 10^{-19}\:\rm C*100\:\rm N/C=-6.2\times 10^{-18}\:N$$

The net force directed upward.

The magnitude $6.2\times 10^{-18}\:\rm N.$