Question

Two small pith balls, each of mass m = 16.6 g, are suspended from the ceiling of the physics lab by 1.8 m long fine strings and are not moving. If the angle which each string makes with the vertical is è = 19°, and the charges on the two balls are equal, what is the magnitude of that charge (in µC)?

Answer 1

If the charged ball is suspended be the string which is deflected by the angle á, the forces acting on it are: mg (downwards), tension T (along the string - to the pivot point), and F (electric force –along the line connecting the charges).
Projections on the horizontal and vertical axes are:
x: T•sin á = F, ….(1)
y: T•cosá = mg. ….(2)
Divide (1) by (2):
T•sin á/ T•cosá = F/mg,
tan á = F/mg.

Since
q1=q2=q.
r=2•L•siná,
k=9•10^9 N•m²/C²
F =k•q1•q2/r² = k•q²/(2•L•siná)².

tan á = F/mg =
= k•q²/(2•L•siná)² •mg.
q = (2•L•siná) • sqrt(m•g•taná/k)=
=(2•1.7•0.506) •sqrt(0.0112•9.8•0.577/9•10^9) =
=4.5•10^-6 C =8182918 ìC.