We are given:
F varies jointly (directly) with q1 and q2, which means that F is proportional to both q1 and q2. also,
F varies inversely with d², so F is inversely proportional to the square to d
Finding a mathemetical experssion:
using the above information, we can say that:
F ∝ q₁
F ∝ q₂
F ∝ 1/(d²)
joining these together, we get:
F ∝ q₁q₂ / d²
let's say that 'k' is the constant of proportionality in this case,
F = k (q₁q₂ / d²)
First case:
F = 8, q₁ = 2, q₂ = 8, d = 4
we can use these values in our expression to find k
[tex]8 = k\frac{2*8}{4^2}[/tex]
[tex]8 = k\frac{16}{16}[/tex]
k = 8
Finding F in the second case:
q₁ = 28, q₂ = 12, d = 2, k = 8
[tex]F = k\frac{q_{1}*q_{2}}{d^2}[/tex]
[tex]F = 8(\frac{28*12}{2^2})[/tex]
[tex]F = 8(\frac{336}{4})[/tex]
[tex]F = 2(336)[/tex]
F = 672 N
