Answer:
1.19×10⁻⁷ C
Explanation:
Draw a free body diagram. Each sphere has three forces acting on it: weight downwards, tension along the string, and electrostatic force horizontally.
Sum of the forces in the y direction:
∑F = ma
T cos 15° − mg = 0
T = mg / cos 15°
Sum of the forces in the x direction:
∑F = ma
T sin 15° − k q² / r² = 0
Substituting and solving for q:
mg tan 15° − k q² / r² = 0
k q² / r² = mg tan 15°
q = r √(mg tan 15° / k)
r, the distance between the spheres, is:
sin 15° = (r/2) / (L/2)
sin 15° = r / L
r = L sin 15°
Given L = 0.600 m, m = 2.00×10⁻³ kg, g = 9.81 m/s², and k = 9×10⁹ Nm²/C²:
q = (0.600 sin 15°) √(2.00×10⁻³ × 9.81 × tan 15° / (9×10⁹))
q = 1.19×10⁻⁷ C
