Compare Magnitude

Question

Compare the magnitude of the electromagnetic and gravitational force between two electrons separated by a distance of 2.00m. Assume the electrons have a mass of 9.11×10^-31kg and a charge of 1.61×10^-19C. Round to the nearest 2 decimal places

Answer 1

Electromagnetic:

 

F_e = kq₁q₂/r₁₂²

 

Gravitational:

 

F_g = Gm₁m₂/r₁₂²

 

Take the ratio of one to the other.  For example, evaluate Fe/Fg.  (The distance will cancel out.)  The result tells you how many times bigger (or smaller) F_e is compared to F_g.

 

F_e/F_g = kq₁q₂ / (Gm₁m₂)

 

q₁ = q₂ = -1.6 x 10^-19 C
k = 9.0 x 10⁹ Nm²/C²

G = 6.67 x 10^-11 Nm²/kg²

m₁ = m₂ = 9.11×10^-31 kg

 

Plug in the numbers and evaluate F_e/F_g.