Electrostatic

Electrostatic Force and Electrostatic Field

A. Electrostatic Force

Attraction or repulsion force between two charges at certain distance.

Unlike charges attract

Like charges repel

Attraction or repulsion force of two charges in empty space is:

\begin{equation*} \begin{split} F & = \frac{1}{4 \pi \varepsilon_o} \: \frac{Q_1 \: Q_2}{r^2} = k \: \frac{Q_1 \: Q_2}{r^2}  \\\\ k & = \frac{1}{4 \pi \varepsilon_o} = 9 \times 10^9 \\\\ \varepsilon_o & = 8,85 \times 10^{-12} \text{ (permitivitas hampa udara)} \end{split} \end{equation*}

When charge in a certain medium, the force is:

\begin{equation*} \begin{split} F_{\text{bahan}} & = \frac{1}{4 \pi \varepsilon_r \: \varepsilon_o} \: \frac{Q_1 \: Q_2}{r^2} = \frac{k}{\varepsilon_r} \: \frac{Q_1 \: Q_2}{r^2} \\\\ F_{\text{bahan}} & = \frac{F_{\text{hampa udara}}}{\varepsilon_r} \\\\ \varepsilon_r & = \text{permitivitas relatif bahan } (\varepsilon_r > 1) \end{split} \end{equation*}

Ratio of force in medium and in vacuum space:

\begin{equation*} \begin{split} \frac{F_{\text{medium}}}{F} & = \frac{\dfrac{\coret [red] {k}}{\varepsilon_r} \: \coret [red] {\dfrac{Q_1 \: Q_2}{r^2}}}{\coret [red] {k} \: \coret [red] {\dfrac{Q_1 \: Q_2}{r^2}}} \\\\ \frac{F_{\text{medium}}}{F} & = \frac{1}{\varepsilon_r} \\ \end{split} \end{equation*}

Because εr > 1, F in medium is lower than in vacuum space.

Electric Field

a region in which an electric charge (a test charge) experiences a force because of influence of another charge.

Electric field pattern of positive charge

Electric field pattern of negative charge

Electric field strength:

$$E = k \: \dfrac{Q}{r^2}$$

When a charge q is in an electric field E, the charge will experience a force:

$F = q \cdot E$