Objects may have a property called electric charge (usually just called charge) (TERM 1). The SI unit of
electric charge is 1 coul**** = 1 C.
(Electric) current is the motion of (electric) charge (TERM 2). The SI unit of electric current is
1 ampere = 1 amp = 1 A: 1 C 1 A·s ( is the mathematical symbol for is defined to equal).
There are two kinds of charge, positive (+) and negative ().
Particle Charge Rest Mass
electron 1.602 × 1019 C 9.109 × 1031 kg (TERM 3)
proton +1.602 × 1019 C 1.673 × 1027 kg (TERM 4)
neutron zero 1.675 × 1027 kg (TERM 5)
Neutral objects have zero total charge, which may result from equal magnitudes of positive and negative
charges. We charge an object by adding or removing electrically-charged particles (usually electrons) (SKILL 1).
Like (i.e., same-sign) charges repel one another. Unlike (i.e., opposite-sign) charges attract one another
(part of SKILL 4). See Figure 21.1, page 793.
A conductor has many charge carriers free to carry current (TERM 6). For example, copper and aluminum
have about 1029 free electrons/m3.
An insulator has hardly any free charge carriers (TERM 7). Examples include glass and rubber.
A semiconductor has some free charge carriers (TERM 8). Example include silicon, germanium, and
gallium arsenide. (SKILL 2)
The principle of conservation of charge is that the total charge in an isolated system does not change
(TERM 9).
The principle of quantization of charge is that the total charge of anything has only certain allowed
values (TERM 10).
Coul****s law is F =
1
40
|q1q2|
r2 (for point charges in vacuum air) (TERM 11) . In this Eq. (21.2):
F is the magnitude of the electric force (in N = newton) on q1 or q2. Recall that the magnitudes of
vectors are never negative. (You find the direction of the force F from like (same-sign) charges repel or
unlike (opposite-sign) charges attract. See Figure 21.9, page 800.)
0 is a constant: 0 = 8.854 × 1012
C2
N·m2 and
1
40 = 8.988 × 109
N·m2
C2 9.0 × 109
N·m2
C2 .
q1 and q2 are the charge values (in C = coul****).
r is the separation (in m = meter) of the point charges (r is never negative).
Cover up the solutions and carefully work Examples 21.1 and 21.2.
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Recall that the total force on a body is the vector sum of the individual forces on it (part of SKILL 5).
Cover up the solution and carefully work Example 21.3. Understand the concepts of Example 21.4.
A charged object attracts a neutral one because, since the unlike charges in the two objects are closer
together and the like charges are farther apart, there is more attraction than repulsion. See Figure 21.7, page 799.
How does an object of charge q attract or repel an object of charge q0?
Step 1: The first object, because it has charge q, sets up an electric field E in the space around that object.
Step 2: The second object, because it has charge q0, experiences a force F0
from that electric field. (SKILL 6)
We define the electric field E at any point to be the electric force per charge
F0

q0 on a test charge q0 placed
at that point: E is in
NC
(TERM 12) . (See Figure 21.13.)
Thus vector equations are E

F0

q0 (21.3) and F0
= q0E (21.4) , where E is an external electric field.
(E is not the electric field of q0 itself).
These vector equations tell us that E and F0
are in the same direction if q0 is positive (+), but E and F0

are in opposite directions if q0 is negative () (part of SKILL 4). See Figure 21.14.
To find the magnitude E of the electric field of a point charge q, we follow the steps on page 808 to arrive at
Eq. (21.6), E =
1
40
|q|
r2 (for a point charge in vacuum air) .
If the charge q is positive (+), the electric field E it sets up is away from it (see Figures 21.15b) and 21.16), but
if the charge q is negative (), the electric field E it sets up is toward it (see Figure 21.15c). (part of SKILL 4)
(Cover up the solution and carefully work Example 21.5. Skip Example 21.6. Understand in Examples 21.7 and
21.8 why the force on the electron is toward the bottom when the external electric field is toward the top.)
The total electric field at any point is the vector sum of the individual electric fields at that point. (part of
SKILL 5) (Cover up the solution and carefully work Example 21.5, skipping the EVALUATE part.)
For a continuous distribution of charge:
1. Find dE for a general dQ using dE =
1
40
|dQ|
r2 .
2. Do a vector integral of dE to find E . (SKILL 7)
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Electric field lines (TERM 13):
1. Used to visualize the electric field. (See many figures in this and following chapters.)
2. E is tangent to an electric field line at any point. See Figure 21.25.
3. E is larger where the lines are closer together (and smaller where farther apart). See Figure 21.26a.
4. A line can be said to start on a positive charge and end on a negative charge. See Figure 21.26b.
An electric dipole is composed of two equal-magnitude, opposite-sign point charges q and q separated
by a distance r (in m). (TERM 14) By definition, p |q|r (q and d changed to |q| and r in Eq. (21.14).)
p is the magnitude of the electric dipole moment p (in C·m) (TERM 15)
|q| is the absolute value of either charge (in C).
The direction of p is from the q to the +q. (SKILL 8) See Figures 21.29 to 21.31.
If an electric dipole is placed in a uniform external electric field E , there is a net torque of = r
× F =
r
× |q|E = |q|r
× E = p
× E . Thus vector Equation (21.16) is = p
× E . (See pages 27 and following
for a vector (cross) product review.) The mathematical evaluation of Eq. (21.16) gives Eq. (21.15) (not actually a
separate equation) for the magnitude of the torque, = pE sin .
is the angle between the directions of the two vectors p and E ; 180° 0.
(tau) is the torque (in N·m). is a vector perpendicular to both p and E in a right-hand sense. See SKILLS
9 and 10. In Figure 21.29, is into the page and in Figure 21.30 is out of the page.
The derivation on pages 821 and 822 shows that U = pE cos = p ·E , Eq. (21.18) and its
mathematical evaluation Eq. (21.17). (See pages 25 and following for a scalar (dot) product review.)
U is the electric potential energy (in J = joule). Being a scalar, U has no direction.
Cover up the solutions and carefully work Examples 21.14 and 21.15.
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