8.4 - Electric Field Lines

8.4.1 - Overview of Electric Field Lines

Earlier we talked about electric fields as a vector quantity represented by the symbol $\mathbf{E}$. Our understanding of electric fields stems from the interactions of positively and negatively charged objects, and the test charge $\mathbf{P}$ which (by scientific convention) is always assumed positive. Based on this assumption, we found out that for a positive test charge P, the direction of $\mathbf{E}$ will face away from a positively charged object. However, it will face a negatively charged one. The magnitude of the electric field $\mathbf{E}$ will be greater when the distance between two particles ($\mathbf{r}$) is smaller as shown by $\mathbf{E} \propto \frac{1}{r^2}$.

There are models that show this concept in the previous module. However, they were only sketched out one dimensionally. In other words, we only represented electric fields as a horizontal line.

Scientist Michael Faraday realized that electric fields are not one dimensional, but rather three dimensional. They extend from a particle in every direction! Faraday eventually developed a useful method for us to visualize these electric fields: electric field lines. Electric field lines are a way for us to look at electric fields in a simple manner while taking into account the characteristics of electric fields.

Key Concepts

In an electric field line diagram:

• Positively charged objects have the electric field lines that radiate outward
• Negatively charged objects have the electric field lines that radiate inward
• The closer you are to the charged object, the denser the set of lines will be
• Dense electric field lines symbolize a stronger field
• The electric field vector $\mathbf{E}$ is always tangent to a field line at any point

warning

Electric field lines are not real. While an electric field itself is real, the lines in the pictures aren’t. The reason for this is because in electric field line models (these are the diagrams of charged particles), there are only a finite amount of lines. This makes it look like the field only exists where those specific lines are. In reality, an electric field is a continuous vector, so the field exists at every point in space around the charge. In other words, at any point around a charged particle, an electric field exists. Therefore, the field would have infinite lines (but obviously, you wouldn’t be able to draw that!).

As you can see, the idea of the electric field $\mathbf{E}$ facing away from a positively charged object, but toward a negatively charged one is still at play here.

Suggested Content

Here is a useful video about drawing electric field lines.

8.4.2 - Analysis of Electric Fields in Dipoles

The linear density of an electric field is proportional to its charge magnitude, an idea represented by $\mathbf{N} = \mathbf{C} q$ such that $\mathbf{N}$ is the number of lines, $\mathbf{q}$ is the charge, and $\mathbf{C}$ is a constant. In other words, the greater the charge, the greater the number of electric field lines!

We can also model the interactions between two charged objects through an electric field when modeling a dipole. A dipole is a system of two charged objects.

Key Concepts

When drawing a diagram for a dipole:

• The electric field lines always flow from positive to negative
• Lines deflect if charged objects repel
• Lines converge if charged objects attract
• If both objects have unequal charges, only some amount of the lines reach the negative charge. The rest are deflected

Below is an example of a dipole:

In summary, electric field lines are visual representations that help us explain the behavior of electric fields in relationship to positively and negatively charged objects.

Useful Resources

8.4.1

• Article about what electric field lines are
• Video about what electric field lines are
• Electric field line properties
  • This article might be locked behind a Sign Up page. You could install a browser extension called "Behind The Overlay" to get around this.
• Field lines article
• Video about drawing field lines (same as Suggested Content)

8.4.2

• Video about electric fields from a dipole
• Dipoles video
• Calculating the electric field of a dipole

Equations and Constants

Equations

• $\mathbf{N} = \mathbf{C} q$
  • $\mathbf{N}$ = the number of lines
  • $\mathbf{q}$ = the charge
  • $\mathbf{C}$ = a constant