Question

Two equally charged, 3.785 g spheres are placed with 2.939 cm between their centers. When released, each begins to accelerate at 281.791 m/s2. What is the magnitude of the charge on each sphere? Express your answer in microCoulombs.

Answer 1

Given

Mass of each sphere, m=3.785 g=0.003785 kg

Distance between them , r=2.939 cm=0.02939 m

The acceleration is

$a=281.791\text{ m/s}^2$

To find

The magnitude of each charge.

Explanation

Let magnitude of each charge be q

The force between two charges is

$F=k\frac{q^2}{r^2}$

Again,

$F=ma$

Comparing these two equations

$\begin{gathered} ma=k\frac{q^2}{r^2} \\ \Rightarrow0.003785\times281.791=9\times10^9\times\frac{q^2}{(0.02939)^2} \\ \Rightarrow q=3.1\times10^{-7}C=0.31mC \end{gathered}$

Conclusion

The magnitude of charge on each sphere is 0.31mC