# Electric Fields I

## Introduction

Electric fields exist in the space around electric charges and are the cause of the electric force.

## Field lines

One can represent electric fields using field lines. The following rules hold for field lines:

• The field lines run from positive pole to negative pole.
• The field lines leave/enter conductors orthogonally to their surface.

The figure on the left shows the field lines of the field between two differently charged metal plates and the figure on the right shows the field of a point charge.

## Electric field $$E$$

Die Eigenschaften eines elektrischen Feldes werden durch die Feldstärke $$E$$ bestimmt. Diese physikalische Größe gibt die Stärke und Richtung des elektrischen Feldes an. A physical quantity for the magnitude and direction of an electric field is \ (E \).

$$E \qquad \qquad \mathrm{Unit:} \qquad \left[ 1 \dfrac{N}{C} \right]$$

Mit dieser Größe kann man die Feldkraft $$F$$, die das Feld auf eine Probeladung mit der Ladung $$q$$ ausübt, berechnen. With this physical quantity you can determine the electric force $$F$$ which the field exerts on a test charge $$q$$.

$$F = E \cdot q$$

### Homogenous field

A homogeneous electric field has the same magnitude and direction at any place.

A good example of a homogeneous field is the field between two charged metal plates. The field strength depends on the voltage $$U$$ and the plate distance $$d$$.

$$E = \dfrac{U}{d} \qquad \Rightarrow \qquad F = E \cdot q = \dfrac{U \cdot q}{d}$$

The following animation shows such a field. (In addition, two test charges are drawn which do not affect the field. They can be moved using the mouse pointer...)

Test charges: $$Q = e$$, $$-e$$     $$Q = 2e$$, $$-2e$$

Show electric field $$E$$ (green)     Show electric force $$F$$ (red)

### Inhomogeneous field

In an inhomogeneous electric field the magnitude and direction at each location varies.

A good example of an inhomogeneous field is the field around a charged metal ball with the charge $$Q$$. The magnitude of the field depends on the distance $$r$$ to the center of the metal ball and the field is directed away from the center of the ball.

$$E = \dfrac{1}{4 \pi \cdot \epsilon_0 \cdot \epsilon_r} \cdot \dfrac{Q}{r^2} \qquad \Rightarrow \qquad F = E \cdot q = \dfrac{1}{4 \pi \cdot \epsilon_0 \cdot \epsilon_r} \cdot \dfrac{Q \cdot q}{r^2}$$

The following animation shows such a field.

Test charges: $$Q = e$$ bzw. $$-e$$     $$Q = 2e$$ bzw. $$-2e$$

Show electric field $$E$$ (green)     Show electric force $$F$$ (red)

## Connection between field lines and electric field

The field lines provide information about the magnitude and direction of the electric field near to a charged body:

• The electric field is always directed orthogonally to the field lines.
• The magnitude of the electric field is greater, the denser the field lines are in one location.

## Visualization of field lines in real world

In dem folgenden Versuch sind rautenförmige Metallteile gitterförmig angeordnet. Setzt man sie einem elektrischen Feld aus, so bilden die Metallteile durch Influenz ein elektrisches Feld aus und drehen sich so dass sie entlang der Feldlinien zeigen. In the following experiment diamond-shaped metal parts are arranged in a grid. When putting them into an electric field, the metal parts form an electric field because of electrostatic induction and rotate so that they point along the field lines.

Structure: Metal plates     Metal ball     Metal balls (+, -)     Metal balls (+, +)

## General visualization of field lines

In the following simulation of the field lines are calculated and displayed for various scenarios. There is also the option to display the magnitude of the electric field.

Structure: Metal plates     Metal ball     Metal balls (+, -)     Metal balls (+, +)

Show field lines     Show electric field

### Sources

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