Question

Two identical small charged spheres hang in equilibrium with equal masses (0.02kg). The length of the strings is equal (0.18m) and the angle with the vertical is identical (7^o). Find the magnitude of the charge on each sphere. The acceleration of gravity is 9.8 m/s^2 and the value of Coulomb

Answer 1

Answer:

The value is $q = 3.4 *10^{-6} \ C$

Explanation:

From the question we are told that

    The mass of each sphere is $m_1 = m_2 = m = 0.020 \ kg$

     The length of the string is  $l = 0.18 \ m$

     The angle of with the vertical is $\theta = 7^o$

      The acceleration due to gravity is $g = 9.8 \ m/s^2$

Generally the force acting between the forces is mathematically represented as

       $F = T cos \theta = \frac{k* q^2}{ r^2}$

=>     $T cos \theta = \frac{k* q^2}{ r^2}$

Generally from Pythagoras theorem the radius of the circular curve created by the force is

         $r = 2 L sin (\theta )$

=>      $r = 2* 0.180 sin (7)$

=>      $r = 0.043 \ m$  

=>     $q = tan \theta * \frac{m * g * r^2 }{k}$

=>      $q = tan(7)* \frac{ 0.02 * 9.8 * 0.043^2 }{9*10^{9}}$

=>      $q = 3.4 *10^{-6} \ C$