A large electroscope is made with \"leaves\" that are 78-cm-long wires with tiny

Question

A large electroscope is made with "leaves" that are 78-cm-long wires with tiny 31 g spheres at the ends. When charged, nearly all the charge resides on the spheres.

Part A

If the wires each make a 26 angle with the vertical (Figure 1) , what total charge Q must have been applied to the electroscope? Ignore the mass of the wires.

Express your answer to two significant figures and include the appropriate units.

C

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Figure 1 of 1

C

Explanation / Answer

The tension in T in each wire is the resultant of the weight Fg = mg and
the electrostatic force between the two spheres Fe = kQ2/r2.
Horizontal component of Tension, Tx = T sin 26o = Fe
Vertical component of Tension , Ty = T cos 26o = Fg
tan 26o = Fe/Fg
Fe = Fg tan26o
kQ2/r2 = mg tan 26o
Q2 = mg tan26o. r2/k
From the trigonometry, r/2 = L sin = 0.78 sin 26 r = 1.56 sin26o
Q = r [mg tan26o/k]
The answer you are looking for is 2Q since each sphere has a charge Q.
2Q = 2r [mg tan26o/k]
Substitute using m = 0.031 kg, k = 8.99 x 109

2Q = 2 x 1.56 x sin 26o x [0.031 x9.81 x tan26o/(8.99 x 10 9)]
= 5.55x10^-6
= 5.5 C (rounded to two significant digits)

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