Question

The mass of a typical car is m=1000kg. so its weight on the Earth’s surface is mg=9800N. Suppose you have two containers, one with N electrons and another with N protons. These two containers are placed a distance 10m apart, and the electric force between them is equal to the weight of the car. Find N.

Answer 1

Every proton will interact with every electron. So the force between 2 boxes will be

$\displaystyle F = \underbrace{\frac{kNq^2}{d^2}}_\text{proton 1 with all electrons} + \underbrace{\frac{kNq^2}{d^2}}_\text{proton 2 with all electrons} + ...+ \underbrace{\frac{kNq^2}{d^2}}_\text{proton N with all electrons} = \frac{kN^2q^2}{d^2}$

$\displaystyle \frac{kN^2q^2}{d^2} =mg$

$\displaystyle N = \sqrt{\frac{mgd^2}{kq^2}} = \sqrt{\frac{9800 \cdot 100}{9 \cdot 10^9 \cdot 2.56 \cdot 10^{-38}}} = 6.522 \cdot 10^{16}$

Answer: $N=6.522 \cdot 10^{16}$