Respuesta :
Explanation:
Let us assume that the carpet is like a large sheet of charge for the dust particle.
Hence, the electric field is as follows.
E = [tex]\frac{\sigma}{2 \epsilon_{o}}[/tex]
Now, the value of [tex]\sigma[/tex] will be as follows.
[tex]\sigma = \frac{-10 \times 10^{-6}}{2 \times 4}[/tex]
= [tex]1.25 \times 10^{-6} C/m^{2}[/tex]
Now, for the dust particle
[tex]F_{net} = F_{e} + mg[/tex] = 0
[tex]F_{e} = -mg[/tex]
qE = mg
Now, putting the given values into the above formula and calculate the charge as follows.
qE = mg
[tex]q \times \frac{1.25 \times 10^{-6} C/m^{2}}{(2 \times 8.854 \times 10^{-12} C^{2}/Nm^}{2})} = 3.0 \times 10^{-9} kg \times 9.8 m/s^{2}[/tex]
q = [tex]416.49 \times 10^{-15} C[/tex]
Thus, we can conclude that charge on the dust particle is [tex]416.49 \times 10^{-15} C[/tex].
