Question

Between two charged particles such as two electrons, which force between them is stronger, the gravitational force of attraction or the electrostatic force?

Hint:

Compare the size of the constants G and k that appear in the formulas for these two forces.

Answer 1

Step 1: Both forces act between two particles and both follow an inverse square law with distance, but their strengths depend on very different properties: mass for gravity and charge for the electric force.

Step 2: The gravitational force between two particles is \( F_g = \dfrac{Gm_1m_2}{r^2} \), where \( G \) is a very small number, about \( 6.67 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \).

Step 3: The electrostatic force between two charges is \( F_e = \dfrac{k q_1 q_2}{r^2} \), where \( k \) is about \( 9 \times 10^{9} \, \text{N m}^2/\text{C}^2 \), a very large number.

Step 4: For two electrons at the same separation, the electrostatic force works out to be roughly \( 10^{42} \) times larger than the gravitational force between them.

Answer: The electrostatic force is far greater than the gravitational force between the same pair of particles.