22.5.2 The Field Model

The basic idea is that the electric field is the agent that exerts an electric force on a charged particle. Or, if you prefer, that charged particles interact via the electric field. We postulate:

  1. Some set of charges, which we call the source charges, alters the space around them by creating an electric field E⃗ at all points in space.

  2. A separate charge q in the electric field experiences force F⃗=qE⃗ exerted by the field. The force on a positive charge is in the direction of E⃗; the force on a negative charge is directed opposite to E⃗.

Thus the source charges exert an electric force on q through the electric field that they’ve created.

We can learn about the electric field by measuring the force on a probe charge q. If, as in FIGURE 22.23a, we place a probe charge at position (x, y, z) and measure force F⃗on q, then the electric field at position (x, y, z) is

E⃗(x, y, z)=F⃗on q at (x, y, z)q (22.5)

We’re defining the electric field as a force-to-charge ratio; hence the units of electric field are newtons per coulomb, or N/C. The magnitude E of the electric field is called the electric field strength.

FIGURE 22.23 Charge q is a probe of the electric field.

The figure labeled (“a”) illustrates the position of a positive point charge labeled q and the force acting on it.
The figure labeled (b) illustrates the position of a point charge and the electrical field line from it.
Full Alternative Text

It is important to recognize that probe charge q allows us to observe the field, but q is not responsible for creating the field. The field was already there, created by the source charges. FIGURE 22.23b shows the field at this point in space after probe charge q has been removed. You could imagine “mapping out” the field by moving charge q all through space.

Because q appears in Equation 22.5, you might think that the electric field depends on the size of the charge used to probe it. It doesn’t. Coulomb’s law tells us that F⃗on q is proportional to q, so the electric field defined in Equation 22.5 is independent of the charge that probes it. The electric field depends only on the source charges that create it.

We can summarize these important ideas with the field model of charge interactions:

MODEL 22.2 Electric field

Charges interact via the electric field.

  • The electric force on a charge is exerted by the electric field.

  • The electric field is created by other charges, the source charges.

    • The electric field is a vector.

    • The field exists at all points in space.

    • A charge does not feel its own field.

  • If the electric field at a point in space is E⃗, a particle with charge q experiences an electric force F⃗on q=qE⃗.

    • The force on a positive charge is in the direction of the field.

    • The force on a negative charge is opposite the direction of the field.

      The figure illustrates the electric field due to a positive source charge.

EXAMPLE 22.6 Electric forces in a cell

Every cell in your body is electrically active in various ways. For example, nerve propagation occurs when large electric fields in the cell membranes of neurons cause ions to move through the cell walls. The field strength in a typical cell membrane is 1.0×107 N/C. What is the magnitude of the electric force on a singly charged calcium ion?

MODEL The ion is a point charge in an electric field. A singly charged ion is missing one electron and has net charge q=+e.

SOLVE A charged particle in an electric field experiences an electric force F⃗on q=qE⃗. In this case, the magnitude of the force is

F=eE=(1.6×10−19 C)(1.0×107 N/C)=1.6×10−12 N

REVIEW This may seem like an incredibly tiny force, but it is applied to a particle with mass m∼10−26 kg. The ion would have an unimaginable acceleration (F/m∼1014 m/s2) were it not for resistive forces as it moves through the membrane. Even so, an ion can cross the cell wall in less than 1 μs.