Question

Two equally charged, 4.433 g spheres are placed with 2.222 cm between their centers. When released, each begins to accelerate at 240.695 m/s2. What is the magnitude of the charge, in micro-Coulombs, on each sphere?

Answer 1

Given:

The mass of the spheres is m1 = m2 = 4.433 g

The distance between the spheres is d = 2.222 cm

The acceleration is a = 240.695 m/s^2

To find the magnitude of the charge in micro-Coulombs.

Explanation:

The magnitude of charge can be calculated by the formula

$F=\frac{kq^2}{d^2}$

The force can be calculated using Newton's law

$\begin{gathered} F=ma \\ =(m1+m2)a \end{gathered}$

On equating the forces, the charges will be

$\begin{gathered} (m_1+m_2)a=\frac{kq^2}{d^2} \\ q=\sqrt{\frac{(m1+m2)ad^2}{k}} \\ =\sqrt{\frac{(4.433\times10^{-3})\times240.695\times(2.22\times10^{-2})^2}{9\times10^9}} \\ =\text{ 2.42}\times10^{-7}\text{ C} \\ =0.242\text{ }\mu\text{ C} \end{gathered}$

Thus, the magnitude of the charge is 0.242 micro Coulomb.