Chapter 16
The Electric Field
Except for fairly simple problems involving a few charges, it’s usually not particularly convenient to use
Coulomb’s law (Eq. (15.1)) directly. One would have to compute all the pairs of forces between each of
the charges making up each of the bodies, which could become a fairly complex calculation. Instead, we
introduce the idea of anelectric fieldas a kind of intermediate quantity. We think of one body as producing
an electric field at each point in space; we can then look at how a second body responds to that electric field.
One reason this is convenient is that we often know what the electric field looks like without necessarily
knowing anything about the distribution of charges that produced the field.
Now let’s define the electric field. The electric field is avector field—it assigns a vector to every point
in space. So let’s imagine you’re standing in a room and wish to find the electric field vector at some point
within the room. You take a smallpositivepoint chargeq 0 (say a proton) and place it at that point, and
measure the electric force on it. Then the electric fieldEis the forceFdivided by the test chargeq 0 :
ED
F
q 0: (16.1)
The electric field vector has units of newtons per coulomb (N/C).
A typical situation is that we will already know the electric field by some other calculation; then Eq.
(16.1) indicates that the force on a chargeqin the electric fieldEisFDqE.
16.1 Electric Field due to a Point Charge
The electric field due to a point chargeqcan be found by using Coulomb’s law. Let’s put a small pos-
itive test chargeq 0 at some distancerfrom the chargeq; then by Coulomb’s law, the force onq 0 is
FD.1=4" 0 /.qq 0 =r^2 /. Dividing byq 0 gives us the electric field due to chargeq:
ED
1
4" 0
q
r^2: (16.2)
16.2 Electric Field Lines
To help visualize the shape of the electric field, in can be helpful to draw diagrams ofelectric field lines.
These lines have the following properties:
- The electric field lines are directed lines (with arrows) that pointfrompositive (C) chargetonegative
() charge.