A large electroscope is made with \"leaves\" that are 70 cm long wires with 24 g

Question

A large electroscope is made with "leaves" that are 70 cm long wires with 24 g spheres at the ends. When charged, nearly all the charge resides on the spheres. If the wires each make a 30° angle with the vertical, what total charge Q must have been applied to the electroscope? Ignore the mass of the wires.
___________________ µC

A large electroscope is made with ''leaves'' that are 70 cm long wires with 24 g spheres at the ends. When charged, nearly all the charge resides on the spheres. If the wires each make a 30 degree angle with the vertical, what total charge Q must have been applied to the electroscope? Ignore the mass of the wires. ___________________ muC

Explanation / Answer

Here ,

let the charge on the spheres is q ,

distance between the charges , d = 2 * 70 * sin(30)

d = 70 cm

let the tension in wire is T

for the right sphere ,

T * cos(30) = m * g

T * cos(30) = 0.024 * 9.8 -------------------(1)

T * sin(30) = k*q^2/d^2

T * sin(30) = 9*10^9 * q^2/0.70^2 ----(2)

solving 1 and 2

tan(30) * 0.024 * 9.8 = 9*10^9 * q^2/0.70^2

solving for q

q = 2.719 *10^-6 C

the charge on each sphere is 2.719 *10^-6 C

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