### Electrolytically Charged Sphere

Part of an apparatus known as a torsion balance, the spheres are electrically charged and the electrostatic force between them is measured by calculating the equilibrium distance between the two charged spheres.

#### Can You Apply It?

- When the spheres in the system are initially charged, the force between them when they are brought near one another is:

\begin{align*}F=(4 \varepsilon \pi a^2)\frac{V_1V_2}{r^2}\end{align*}

where \begin{align*}a\end{align*}

\begin{align*}\tau=k\theta\end{align*}

- The torque is a result of the force that is applied to the sphere over a distance \begin{align*}l\end{align*}
l , from the axis of rotation. This force takes the form of

\begin{align*}F=\frac{k}{l}\theta\end{align*}

#### Show What You Know

- What relationship exists between the angle of deflection and the voltage applied to the spheres?
- As the distance between the charged spheres increases, what do you expect to happen to the angle of deflection?
- What assumption is being made about the torque equation? (Hint: think about the angle between the force and the lever arm.)