Determine the separation at which two equal charges of 1.0 C each must be placed so that the force between them is equal to the weight of a 50 kg person.

Step-by-step solution

The electrostatic force between two charges is given by Coulomb's law: F = 1 4 ₀ q₁ q₂ r^2 The weight of the person is given by: W = mg Equating the electrostatic force to the weight of the person: 1 4 ₀ q₁ q₂ r^2 = mg Substituting the given values ( q₁ = q₂ = 1.0 C , m = 50 kg , g = 9.8 m/s ^2 , 1 4 ₀ = 9 10^9 N m ^2/ C ^2 ): 9 10^9 1.0 1.0 r^2 = 50 9.8 9 10^9 r^2 = 490 r^2 = 9 10^9 490 = 900 49 10^6 r = 30 7 10^3 4.28 10^3 m Rounding to two significant figures, we get 4.3 10^3 m .