Electric field lines can offer another way of visualizing the electric field to help us better understand how charge affects the space around it. Additionally, electric field lines can help us understand the force that a charge will feel if placed in an electric field. Let’s establish some rules for understanding electric field lines and how we can use them to understand the magnitude and direction of the electric field around a charge or charge distribution. Recall that we can move to any point in three dimensions of space around a charge and there will be an electric field vector at that point.
Electric field lines, like vectors, are denoted by lines with arrowheads. However, electric field lines can curve in space.
We can find the direction of the electric field vector at any point by drawing a vector tangent to the electric field lines. These vectors are what you have seen previously, in Electric Field Vector Maps.
The density of the electric field lines indicate the magnitude of the field at that point. Very closely spaced electric field lines indicates a larger field magnitude and very sparsely spaced lines indicates a smaller field magnitude.
Electric field lines generated by charged particles start on positive charges and end on negative charges, or at infinity if we assume no other charges exist in the system.
Since electric fields are vector fields, electric field lines never cross. If there were two electric field vectors at a single point in space, the principle of superposition would dictate that they add as a vector sum.
Figure20.7.1.A visualization of the electric field of a positive point charge.
Figure20.7.2.A visualization of the electric field of a negative point charge.
The electric field of a positive point charge points away from the charge and reduces in magnitude with the inverse square of distance from the charge. The electric field of a negative charge points toward the charge and also has a magnitude that decreases with the inverse square of the distance from that charge. The field of a negative point charge and a negative point mass have identical shape, but differ in the numerical value associated with the field. We saw in previous activities that the magnitude of the electric force is much, much larger than that of the gravitational force.
Using the shape of the field from a single point charge, and vector superposition, we can infer the electric field from other charge distributions. Some common geometries of charge we will consider are those of lines of charge, cylinders, cylindrical shells, circles, spheres, spherical shells, sheets and solid rectangles. Now might be a good time to review how to calculate basic geometric quantities such as circumference, surface area and volumes of these common geometries.
ExercisesActivities
1.Field Lines.
Using the shape of the field from a single point charge, and vector superposition, sketch the shape of the following charge geometries:
An electric dipole.
A one dimensional line of positive charge.
A sphere of negative charge.
A hallow sphere of positive charge.
2.Field Line Simulation.
Use this electric field simulation to help you understand the shape electric field lines take around various charges or charge distributions. Do the electric field lines you sketched previously agree with the simulation?
