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## Homework Statement

A large electroscope is made with "leaves" that are [itex]78[/itex]-cm-long wires with tiny [itex]24[/itex]-g spheres at the ends. When charged, nearly all the charge resides on the spheres.

If the wires each make a [itex]26^{\circ}[/itex] angle with the vertical, what total charge [itex]Q[/itex] must have been applied to the electroscope? Ignore the mass of the wires.

## Homework Equations

[itex]F = mg[/itex]

[itex]F = \dfrac{kq_1q_2}{r^2}[/itex]

## The Attempt at a Solution

Tried this way:

[itex]F_{\text{electrostatic}} = F_{\text{gravity}}[/itex]

[itex]\dfrac{k(\frac{Q}{2}(\frac{Q}{2}))}{r^2} = mg\cos(\theta)[/itex]

[itex]r = 2L\sin(\theta) [/itex] is the distance between the two spheres and the length of the string, so we have

[itex]Q = 4L\sin(\theta)\sqrt{\dfrac{mg\cos(\theta)}{k}} \approx 6.63 \times 10^{-6} C[/itex]

But the answer is wrong.