Physics Question

Question

Demonstrate with Coulomb’s Law what happens to the magnitude of the force between two charges Q1 and Q2 separated by a distance R if:
a) one of the charges is doubled?

b) both of the charges are doubled?

c) separation distance is doubled?

d) both charges are doubled and separation distance is doubled?

Answer 1

F = kQ₁Q₂/R²

 

(a)

 

Replace Q₁ with 2Q₁

 

F' = k(2Q₁)Q₂/R² = 2(kQ₁Q₂/R²) = 2F

 

(b)

 

Replace Q₁ with 2Q₁ and Q₂ with 2Q₂

 

F' = k(2Q₁)(2Q₂)/R² = 4(kQ₁Q₂/R²) = 4F

 

(c)

 

Replace R with 2R

 

F' = kQ₁Q₂/(2R)² = (1/4)(kQ₁Q₂/R²) = (1/4)F

 

(d)

 

Replace Q₁ with 2Q₁, Q₂ with 2Q₂, and R with 2R

 

F' = k(2Q₁)(2Q₂)/(2R)² = (4/4)(kQ₁Q₂/R²) = 1F = F