# Introduction

Interactive 5.1.1

It is often useful to have a visual representation of the electric field in a region, in order to develop a more intuitive picture of what's going on. As the electric field is a vector field, we can begin by drawing little arrows showing where the electric field points at various positions. Of course, we can't draw an arrow at every point, but we will draw enough of them to give the general sense of things.

Drawing this many arrows can get to be a chore, however, so instead let's connect the arrows together into smooth lines, which we'll call electric field lines. Each field line has a direction associated with it, and if you want to know the direction of the electric field at any point along the field line, you simply find the tangent. (You might notice that by going from arrows to lines that we seem to have lost information about the magnitude of the electric field; however, we will see that this information can still be obtained.)

When given one or more source charges, the electric field lines can be determined by asking "What Would a Proton Do?" The field lines always point in the direction a positive charge would be pushed or pulled. For example, the field lines created by a positive source charge (as in the figure) point directly away from it, because a positive target charge would be repelled by the positive source. A positive target would be attracted to a negative source, however, and so field lines point inward in that case. We say that these field lines are radial because they extend outward (or inward) like the rays of the sun.

Interactive 5.1.2
When we have multiple sources, the field lines correspond to the net electric field: that is, the vector sum of the electric fields by all the sources. The figure to the left shows two positive source charges of equal magnitude and the field lines they generate together; clicking a green button will show how that field is calculated.
Interactive 5.1.3

The figure to the right shows the same field. Notice that close to each individual charge, the electric field is radial, sticking straight out of the point charge. When we are close to a charge, its field is so much stronger than any other field that it is as if the other charges didn't exist.

At the other extreme, if we move very far away from both charges, then the charges start to blur together and look like a single charge, and the electric field lines behave as if coming from a single point charge (with total charge equal to the charge of the system). An exception occurs if the net charge of the system is zero, as it is for the dipole (that is, two equal and opposite charges) pictured in the following figure. The electric field does not eventually become radial, but instead adopts a characteristic lobed shape.

### Dipole Field

To summarize the features of an electric field line diagram:
• The electric field is tangent to the field lines at any point.
• Field lines always have a direction.
• Field lines start at positive charges, and end at negative charges.
• Field lines close to a charge look like the field of a single charge (that is, they are radial).
• Field lines far from a set of charges (with total charge Q) look like the field lines of a single point charge Q, unless Q = 0.
• Field lines diverge as the field gets weaker, and converge as the field gets stronger.
You can use the following applet to explore the fields generated by various charges.
Interactive 5.1.4