posted by Becky .
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)?
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.
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.