Given:
The mass of the spheres is m = 4.982 g
The distance between the center of spheres is d = 3.173 cm
The acceleration is a = 258.312 m/s^2.
To find the magnitude of charge in micro Coulomb on each sphere.
Explanation:
According to Newton's second law, the force will be
[tex]F\text{ =ma}[/tex]According to Coulomb's law, the force will be
[tex]F=\frac{kq^2}{r^2}[/tex]Here, k is the Coulomb's constant whose value is
[tex]k=9\times10^9\text{ N m}^2\text{ /C}^2[/tex]On equating the forces, the charge will be
[tex]\begin{gathered} ma=\frac{kq^2}{r^2} \\ q=\sqrt{\frac{mar^2}{k}} \end{gathered}[/tex]On substituting the values, the magnitude of charge will be
[tex]\begin{gathered} q=\sqrt{\frac{(4.982\times10^{-3})\times258.312\times(3.173\times10^{-2})^2}{9\times10^9}} \\ =3.79\text{ }\times10^{-7}\text{ C} \\ =0.379\text{ }\times10^{-6}\text{ C} \\ =0.379\text{ }\mu C \end{gathered}[/tex]The magnitude of the charge of each sphere is 0.379 microCoulomb
