Need help with physics problem

Question

Charge q2 in the figure is in equilibrium. Assume q = 5.4 nC.

(+)

q1 q q2

<-----------------------><----------------------->

10 cm 10 cm

What is q1?

Any help would be appreaciated.

Answer 1

For equilibrium the electrostatic forces need to balance. For the electrostatic force you can use Coulomb's Law and you can add the force from each charge separately. In the x-direction

F_net = k q⋅q₂/r² + k q₂⋅q₁/(2r)² = 0. Solving for q₁ gives q₁ = -4 q ≈ -21.6 nC.