![]() The three-dimensional version of this map is obtained by rotating this map about the axis that goes through both charges. In other words, electric-field lines cannot cross each other.įigure 18.19(a) shows a two-dimensional map of the electric field generated by a charge of + q and a nearby charge of − q. Because this sum can only be a single number, we know that only a single electric-field line can go through any given point. The electric field due to multiple charges may be found by adding together the electric field from each individual charge. The field lines are denser as you approach the point charge.Įlectric-field maps can be made for several charges or for more complicated charge distributions. The arrows point in the direction that a positive test charge would move. The red point on the left carries a charge of +1 nC, and the blue point on the right carries a charge of –1 nC. In fact, the density of the electric field lines is proportional to the strength of the electric field!įigure 18.18 Electric field lines from two point charges. Looking at Figure 18.17 and Figure 18.18 again, we see that the electric field lines become denser as we approach the charge that generates it. For example, at 2 cm from the charge Q ( r = 2 cm), the electric field is four times stronger than at 4 cm from the charge ( r = 4 cm). The equation E = k | Q | / r 2 E = k | Q | / r 2 says that the electric field gets stronger as we approach the charge that generates it. Thus, the direction of the electric field lines is consistent with what we find by using Coulomb’s law. The opposite is true for negative test charges. If we place the positive charge in the electric field of the negative charge, the positive charge is attracted to the negative charge. This is consistent with Coulomb’s law, which says that like charges repel each other. Thus, a positive test charge placed in the electric field of the positive charge will be repelled. Notice that the electric field lines point away from the positive charge and toward the negative charge. On the left is the electric field created by a positive charge, and on the right is the electric field created by a negative charge. Just drawing the electric field lines in a plane that slices through the charge gives the two-dimensional electric-field maps shown in Figure 18.18. Ask whether students can use this to show that the number of field lines crossing a surface per unit area shows that the electric field strength decreases as the inverse square of the distance. Point out that the number of lines crossing an imaginary sphere surrounding the charge is the same no matter what size sphere you choose. Point out that all electric field lines originate from the charge. Mathematically, saying that electric field is the force per unit charge is written as For example, if we double the charge of the test charge, the force exerted on it doubles. The force exerted is proportional to the charge of the test charge. The electric field exerts a force on the test charge in a given direction. A test charge is a positive electric charge whose charge is so small that it does not significantly disturb the charges that create the electric field. Now consider placing a test charge in the field. The electric field extends into space around the charge distribution. The charge distribution could be a single point charge a distribution of charge over, say, a flat plate or a more complex distribution of charge. If you know the electric field, then you can easily calculate the force (magnitude and direction) applied to any electric charge that you place in the field.Īn electric field is generated by electric charge and tells us the force per unit charge at all locations in space around a charge distribution. Michael Faraday, an English physicist of the nineteenth century, proposed the concept of an electric field. For example, the gravitational field surrounding Earth and all other masses represents the gravitational force that would be experienced if another mass were placed at a given point within the field. The concept of a field is very useful in physics, although it differs somewhat from what you see in movies.Ī field is a way of conceptualizing and mapping the force that surrounds any object and acts on another object at a distance without apparent physical connection. You may have heard of a force field in science fiction movies, where such fields apply forces at particular positions in space to keep a villain trapped or to protect a spaceship from enemy fire. Explain that electric fields are very similar to gravitational fields. Describe how gravity can be thought of as a field that surrounds a mass and with which other masses interact. Ask students whether they have seen movies that use the concept of fields as in force fields.
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