5.4 Electric field  (Page 2/7)

To push the analogy further, notice the units of the electric field: From $F=QE$ , the units of E are newtons per coulomb, N/C, that is, the electric field applies a force on each unit charge. Now notice the units of g : From $w=mg$ , the units of g are newtons per kilogram, N/kg, that is, the gravitational field applies a force on each unit mass. We could say that the gravitational field of Earth, near Earth’s surface, has a value of 9.81 N/kg.

The meaning of “field”

Recall from your studies of gravity that the word “field” in this context has a precise meaning. A field, in physics, is a physical quantity whose value depends on (is a function of) position, relative to the source of the field. In the case of the electric field, [link] shows that the value of $\overrightarrow{\text{E}}$ (both the magnitude and the direction) depends on where in space the point P is located, measured from the locations ${\overrightarrow{\text{r}}}_i$ of the source charges $q_i$ .

In addition, since the electric field is a vector quantity, the electric field is referred to as a vector field . (The gravitational field is also a vector field.) In contrast, a field that has only a magnitude at every point is a scalar field . The temperature in a room is an example of a scalar field. It is a field because the temperature, in general, is different at different locations in the room, and it is a scalar field because temperature is a scalar quantity.

Also, as you did with the gravitational field of an object with mass, you should picture the electric field of a charge-bearing object (the source charge) as a continuous, immaterial substance that surrounds the source charge, filling all of space—in principle, to $\text{±}\infty$ in all directions. The field exists at every physical point in space. To put it another way, the electric charge on an object alters the space around the charged object in such a way that all other electrically charged objects in space experience an electric force as a result of being in that field. The electric field, then, is the mechanism by which the electric properties of the source charge are transmitted to and through the rest of the universe. (Again, the range of the electric force is infinite.)

We will see in subsequent chapters that the speed at which electrical phenomena travel is the same as the speed of light. There is a deep connection between the electric field and light.

Superposition

Yet another experimental fact about the field is that it obeys the superposition principle. In this context, that means that we can (in principle) calculate the total electric field of many source charges by calculating the electric field of only $q_1$ at position P , then calculate the field of $q_2$ at P , while—and this is the crucial idea—ignoring the field of, and indeed even the existence of, $q_1.$ We can repeat this process, calculating the field of each individual source charge, independently of the existence of any of the other charges. The total electric field, then, is the vector sum of all these fields. That, in essence, is what [link] says.

In the next section, we describe how to determine the shape of an electric field of a source charge distribution and how to sketch it.