Find charges of q2 and q3 on an equilateral triangle with known electric forces.

Question

Three point charges q1, q2 and q3 are located at the corners of an equilateral triangle with sides of 10 cm. The electrical forces between them are F12= 5.4 N (attractive), F13= 15 N (repulsive) and F23= 9 N (attractive). Given that q1 is negative, what are the values of q2 and q3?

(Answer: q2= 1.89 μC and q3= -5.28 μC)

Answer 1

As Q1 is negative and F₁₂ is attractive, that means Q₂ is positive; as Q1 is negative and F₁₃ repulsive, that means Q₃ is negative;

Now, use Coulomb’s law:

F₁₂=kQ₁Q₂/0.01 =5.4 N;

F₁₃=kQ₁Q₃/0.01 =15 N;

F₂₃=kQ₂Q₃/0.01 =9 N;

 Dividing gives (F₁₃/ F₁₂₎₌ Q₃/Q₂=15/5.4≈2.78 , and then Q₃=2.78Q₂

Now, substitute Q₃=2.77Q₂ into F₂₃  kQ₂²2.77/0.01 =9 , and then Q₂≈1.89µC;

and Q₃=-2.77Q₂=-1.89*2.78 µC=-5.28 µC