Question

Calculate the Coulomb’s force between proton and electron separated by a distance of \( 0.8 \times 10^{-15} \) m.

Hint:

Coulomb’s force is inversely proportional to the square of the distance between the charges.

Answer 1

Step 1: Using Coulomb’s law.
Coulomb’s law gives the force between two point charges \( q_1 \) and \( q_2 \) separated by a distance \( r \): \[ F = k \frac{|q_1 q_2|}{r^2} \] where \( k = 9 \times 10^9 \, \text{N·m}^2/\text{C}^2 \) is Coulomb's constant, \( q_1 \) and \( q_2 \) are the charges, and \( r \) is the distance between them.
Step 2: Substituting values.
The charge on a proton and electron is \( e = 1.6 \times 10^{-19} \, \text{C} \). The distance \( r = 0.8 \times 10^{-15} \, \text{m} \). Substituting these values into Coulomb's law: \[ F = 9 \times 10^9 \frac{(1.6 \times 10^{-19})^2}{(0.8 \times 10^{-15})^2} \] \[ F = 9 \times 10^9 \frac{2.56 \times 10^{-38}}{6.4 \times 10^{-30}} = 3.6 \times 10^{-8} \, \text{N} \] Step 3: Conclusion.
Thus, the Coulomb force between the proton and electron is \( 3.6 \times 10^{-8} \, \text{N} \).