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.

Step-by-step explanation

Let magnitude of each charge be q

The force between two charges is

`F=k(q^2)/(r^2)`

Again,

`F=ma`

Comparing these two equations

`\begin{gathered} ma=k(q^2)/(r^2) \\ \Rightarrow0.003785*281.791=9*10^9*(q^2)/((0.02939)^2) \\ \Rightarrow q=3.1*10^(-7)C=0.31mC \end{gathered}`

Conclusion

The magnitude of charge on each sphere is 0.31mC