Question

Rocket observations show that dust particles in Earth's upper atmosphere are often electrically charged.

(a) Find the distance separating two dust particles (in m) if each has a charge of +e and the Coulomb force between them has magnitude 1.65 ✕ 10^−14 N.

m

(b) Calculate the mass (in kg) of one of the dust particles if this Coulomb force would accelerate it at 2.60 ✕ 10^8 m/s^2. (In the upper atmosphere, effects from other nearby charges typically result in a small net force and acceleration.)

kg

Answer 1

a)

Coulomb force between the two dust particles is $F=\frac{q_1q_2}{4\pi\epsilon_0 r^2}$

Charge on each dust particle is $q_1=q_2=+e=+1.6*10^{-19}\,C$

Distance between the dust particles is $r$

$F=1.65*10^{-14}\,N$

$r=\sqrt{\frac{q_1q_2}{4\pi\epsilon_0 F}}$

$r=\sqrt{8.99*10^9*\frac{(1.6*10^{-19})^2}{ 1.65*10^{-14}}}=1.18*10^{-7}\,m$

Distance between the dust particles is $r=1.18*10^{-7}\,m$

b)

Acceleration of particle is $a={2.60*10^8}\,m/s^2$

$F=ma$

Mass of the dust particle is $m=\frac{F}{a}=\frac{1.65*10^{-14}}{2.60*10^8}=6.35*10^{-23}\,kg$