Question

The electrostatic force that a charged particle, q1q1 , exerts on another charged particle, QQ , at a distance r1r1 , is FF . A second charged particle, q2q2 , exerts the same force FF on QQ at half the distance r1r1 . What is the value of q1q1 in relation to q2q2 ?

Answer 1

q₁ / q₂ = 4

Step-by-step explanation:

In this exercise we must use Coulomb's law

F = k q₁q₂ / r²

For this case the electric force is

F = k q₁ Q / r₁²

indicate that another particle q₂ has the same force on Q, but for r₂ = r₁ /2

F = k q₂ Q / r₂²

we equate the two equations

q₁Q / r₁² = q₂ Q / r₂²

we substitute r₂

q₁Q / r₁² = q₂ Q / (r₁/2)²

q₁ = q₂ 4

the relationship between the two charges is

q₁ / q₂ = 4