Posted by **Becky** on Wednesday, June 6, 2012 at 11:44am.

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)?

- physics -
**Tim Korenman**, Wednesday, June 6, 2012 at 11:48am
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.

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