<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
You are viewing an older version of this Concept. Go to the latest version.

# Electric Charge and Electric Force

## Charge is created by electron imbalance; like charges repel while opposite charges attract.

Estimated5 minsto complete
%
Progress
Practice Electric Charge and Electric Force
Progress
Estimated5 minsto complete
%
Electrolytically Charged Sphere

### Electrolytically Charged Sphere

Credit: Eorlingas
Source: http://commons.wikimedia.org/wiki/File:Pendule_de_torsion.png

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:

F=(4επa2)V1V2r2\begin{align*}F=(4 \varepsilon \pi a^2)\frac{V_1V_2}{r^2}\end{align*}

where a\begin{align*}a\end{align*} is the radius of each of the spheres, V1\begin{align*}V_1\end{align*} and V2\begin{align*}V_2\end{align*} are the respective voltages and r\begin{align*}r\end{align*} is the distance between the center of the spheres. One of the spheres is attached to a torsion spring that is calibrated to measure the to angle of deflection from equilibrium when a torque τ\begin{align*}\tau\end{align*} is applied. The spring is tightened to bring the charged sphere back to equilibrium, at which point the angle is measured. For small displacements the torque is related to the angle by

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

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

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

#### Show What You Know

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

### My Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes