Respuesta :
Given:
The mass of the first sphere is: m1 = 3.699 g.
The mass of the second sphere is: m2 = 3.699 g
The distance between their centers is: d = 3.592 cm
The acceleration of each sphere is: a = 297.727 m/s^2
To find:
Since the spheres are identical in their masses, the force on each sphere is:
[tex]F=ma[/tex]Substitute the values in the above equation and simplify it, we get:
[tex]\begin{gathered} F=3.699\text{ g}\times297.727\text{ m/s}^2 \\ \\ F=3.699\text{ g }\times\frac{1\text{ kg}}{1000\text{ g}}\times297.727\text{ m/s}^2 \\ \\ F=3.699\times10^{-3}\text{ kg}\times297.727\text{ m/s}^2 \\ \\ F=1.1012\text{ N} \end{gathered}[/tex]This is the force experienced by each sphere and is has a magnitude equal to the magnitude of the electrostatic force.
The electrostatic force of attraction or repulsion between two charges is given by:
[tex]F=\frac{1}{4\pi\epsilon_0}\frac{q^2}{r^2}[/tex]Substitute the values in the above equation and simplify it, we get:
[tex]\begin{gathered} 1.1012\text{ N}=\frac{9\times10^9\text{ N}\cdot m^2\text{/C}^2\times q^2}{(3.592\text{ cm})^2} \\ \\ 1.1012\text{ N}=\frac{9\times10^9\text{ N}\cdot m^2\text{ / C}^2\times q^2}{(3.592\text{ cm}\times\frac{1\text{ m}}{100\text{ cm}})^2} \\ \\ 1.1012\text{ N}=\frac{9\times10^9\text{ N}\cdot m^2\text{ /C}^2\times q^2}{(3.592\times10^{-2})^2\text{ m}^2} \\ \\ 1.1012\text{ N}=\frac{9\times10^9\text{ N.m}^2\text{/C}^2\times q^2}{1.2902\times10^{-3}\text{ m}^2\text{ }} \\ \\ 1.1012\text{ N}=6.9757\times10^{12}\text{ N/C}^2\times q^2 \\ \\ \end{gathered}[/tex]Rearranging the above equation and simplify it, we get:
[tex]\begin{gathered} q^2=\frac{1.1012\text{ N}}{6.9757\times10^{12}\text{ N/C}^2} \\ \\ q=\sqrt{1.5786\times10^{-13}\text{ C}^2} \\ \\ q=0.3973\times10^{-6}\text{ C} \\ \\ q=0.3973\text{ }\mu\text{C} \end{gathered}[/tex]Final answer:
The magnitude of the charge on each sphere is 0.3973 microcolumns.
