Coulomb's Law in Numbers: Hydrogen and Millikan's Oil Drop

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1. Question 1

   Use $k_e = 8.99\times10^{9}\ \text{N}\,\text{m}^2/\text{C}^2$. With $e = 1.602\times10^{-19}\ \text{C}$, find the electric force between an electron and a proton $1.0\times10^{-10}\ \text{m}$ apart, in units of $10^{-8}\ \text{N}$ to three significant figures.

   $F =$×10⁻⁸ N

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2. Question 2

   Use $k_e = 8.99\times10^{9}\ \text{N}\,\text{m}^2/\text{C}^2$. With $e = 1.602\times10^{-19}\ \text{C}$, find the magnitude of a proton's electric field $2.0\times10^{-10}\ \text{m}$ from it, in units of $10^{10}\ \text{N/C}$ to three significant figures.

   $E =$×10¹⁰ N/C

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3. Question 3

   Use $k_e = 8.99\times10^{9}\ \text{N}\,\text{m}^2/\text{C}^2$, $G = 6.674\times10^{-11}\ \text{N}\,\text{m}^2/\text{kg}^2$, $e = 1.602\times10^{-19}\ \text{C}$, $m_e = 9.11\times10^{-31}\ \text{kg}$. Find $F_e/F_g$ for two electrons, in units of $10^{42}$ to two significant figures.

   $F_e/F_g =$×10⁴²

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4. Question 4

   An oil drop of radius $1.5\ \mu\text{m}$ and density $880\ \text{kg/m}^3$ carries charge $Q = -4e$, with $e = 1.602\times10^{-19}\ \text{C}$ and $g = 9.8\ \text{m/s}^2$. Taking $+y$ upward, find the field component $E_y$ (with its sign) that holds the drop still, in units of $10^{5}\ \text{N/C}$ to three significant figures.

   $E_y =$×10⁵ N/C

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5. Question 5

   An oil drop of mass $2.0\times10^{-15}\ \text{kg}$ hangs still in a downward field of magnitude $4.08\times10^{4}\ \text{N/C}$. With $g = 9.8\ \text{m/s}^2$ and $e = 1.602\times10^{-19}\ \text{C}$, how many excess electrons does it carry?

   $n =$

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