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1 year ago with 94 notes

Electric Field Lines

Electromagnetism is a difficult topic in physics because the concepts aren’t easy to visualize. We’ve been introduced to positive and negative charges and the interaction across space between two charges. Electric fields can be tricky to imagine, stimulating to wonder about especially in the off-topic, subjective idea of touch (we’ll visit this later), and yet there’s one more thing to add on to the complicated mess; electric field lines.

Now, an electric field line is an important, imaginary line that will aid us in visualizing and understanding electric fields.

An electric field line is an imaginary line that is drawn through a region of space where its tangent is in the direction of the electric field vector. Although first called “lines of force” by Michael Faraday we now refer to them as field lines.

Just as we take careful measures when drawing vectors we will typically draw field lines in such ways to indicate magnitudes at certain points; we draw vectors with hats and scalars as bold-faced, stick to one method of drawing so as to not confuse your short hand methods.

Electric field lines show the direction ofimagewith their spacing indicating the magnitude of the vector at each point. Whereverimageis strong we typically draw our lines close together; where it is weak we draw our lines spaced out. We should note that at any point the electric field has its own unique direction, meaning field lines never intersect.

Another thing to remember is in what directions our field lines are to be drawn. We take positive charges to have outward facing field lines, and negative charges to have inward facing field lines. (Perhaps a useful way to remember this is “positive points out”, recognizing that “positive” and “out” have the letter ‘O’ where negative does not.) 

To eliminate complexity we will typically only see field lines drawn in two dimensions with a few lines, but understand that they are realistically in three dimensions and contain an infinite number of lines.

The planes in which we draw our electric field lines are called field maps, and can be referred to as cross sections of three dimensional patterns. In the first image the image field vector is drawn along the tangents of the field lines. In the second image these vectors are labeled for easier viewing. Make notice that in general the magnitude of the electric field is different at any point on a given field line. Do not think that a field line is a measure of a constant electric field magnitude.

Now is a good time to remember how field lines are drawn according to magnitudes. The second image shows a situation where the field magnitude is large between the charges. Field lines are drawn close together towards the middle of the picture, but are drawn loosely and spaced out beyond the middle. This indicates a large field magnitude between the charges and a small field magnitude in the region beyond the charges.

This can also be visualized in a field map of two like charges, the concept will just be in reverse; there will be a small field magnitude between the charges as opposed to a large magnitude. 

Field lines can also be straight, parallel, and uniformly spaced. We call this a uniform field and it can be seen between two parallel conducting plates.

Image Credit: webassign

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