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Answer:
The value is [tex]q = 3.4 *10^{-6} \ C[/tex]
Explanation:
From the question we are told that
The mass of each sphere is [tex]m_1 = m_2 = m = 0.020 \ kg[/tex]
The length of the string is [tex]l = 0.18 \ m[/tex]
The angle of with the vertical is [tex]\theta = 7^o[/tex]
The acceleration due to gravity is [tex]g = 9.8 \ m/s^2[/tex]
Generally the force acting between the forces is mathematically represented as
[tex]F = T cos \theta = \frac{k* q^2}{ r^2}[/tex]
=> [tex]T cos \theta = \frac{k* q^2}{ r^2}[/tex]
Generally from Pythagoras theorem the radius of the circular curve created by the force is
[tex]r = 2 L sin (\theta )[/tex]
=> [tex]r = 2* 0.180 sin (7)[/tex]
=> [tex]r = 0.043 \ m[/tex]
=> [tex]q = tan \theta * \frac{m * g * r^2 }{k}[/tex]
=> [tex]q = tan(7)* \frac{ 0.02 * 9.8 * 0.043^2 }{9*10^{9}}[/tex]
=> [tex]q = 3.4 *10^{-6} \ C[/tex]