Fisica

23
Electric Fields
CHAPTER OUTLINE
23.1
23.2
23.3
23.4
23.5
23.6
23.7

Properties of Electric
Charges
Charging Objects by
Induction
Coulomb’s Law
The Electric Field
Electric Field of a
Continuous Charge Distribution
Electric Field Lines
Motion of a Charged Particle
in a Uniform Electric Field

ANSWERS TO QUESTIONS
Q23.1

A neutral atom is one that has no net charge. Thismeans that it has the same number of electrons
orbiting the nucleus as it has protons in the nucleus.
A negatively charged atom has one or more excess
electrons.

*Q23.2

(i) Suppose the positive charge has the large value 1 m C.
The object has lost some of its conduction electrons,
in number 10−6 C (1 e/1.60 × 10−19 C) = 6.25 × 1012 and
in mass 6.25 × 1012 (9.11 × 10−31 kg) = 5.69 ×10−18 kg.
This is on the order of 1014 times smaller than the
~1g mass of the coin, so it is an immeasurably small
change. Answer (d).
(ii) The coin gains extra electrons, gaining mass on
the order of 10−14 times its original mass for the charge
−1 m C. Answer (b).

Q23.3

All of the constituents of air are nonpolar except for water. The polar water molecules in the
air quite readily“steal” charge from a charged object, as any physics teacher trying to perform
electrostatics demonstrations in the summer well knows. As a result—it is difficult to accumulate
large amounts of excess charge on an object in a humid climate. During a North American
winter, the cold, dry air allows accumulation of significant excess charge, giving the potential
(pun intended) for a shocking (pun alsointended) introduction to static electricity sparks.

Q23.4

Similarities: A force of gravity is proportional to the product of the intrinsic properties (masses)
of two particles, and inversely proportional to the square of the separation distance. An electrical
force exhibits the same proportionalities, with charge as the intrinsic property.
Differences: The electrical force can eitherattract or repel, while the gravitational force as
described by Newton’s law can only attract. The electrical force between elementary particles is
vastly stronger than the gravitational force.

Q23.5

No. The balloon induces polarization of the molecules in the wall, so that a layer of positive
charge exists near the balloon. This is just like the situation in Figure 23.4a, except that thesigns
of the charges are reversed. The attraction between these charges and the negative charges on the
balloon is stronger than the repulsion between the negative charges on the balloon and the
negative charges in the polarized molecules (because they are farther from the balloon), so that
there is a net attractive force toward the wall. Ionization processes in the air surrounding the
balloonprovide ions to which excess electrons in the balloon can transfer, reducing the charge
on the balloon and eventually causing the attractive force to be insufficient to support the weight
of the balloon.

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Chapter 23

*Q23.6 Answer (c). Each charge produces field as if it were alone in the Universe.
*Q23.7 (i) According to the inverse square law, the field is one-fourth as large attwice the distance. The
answer is (c), 2 × 36 cm = 72 cm.
(ii) The field is four times stronger at half the distance away from the charge. Answer (b).
Q23.8

An electric field created by a positive or negative charge extends in all directions from the charge.
Thus, it exists in empty space if that is what surrounds the charge. There is no material at point A
in Figure 23.21(a), so there is nocharge, nor is there a force. There would be a force if a charge
were present at point A, however. A field does exist at point A.

*Q23.9 (i) We compute qAqB/r2 in each case. In (a) it is 400/4 = 100 (nC/cm)2. In (b) and (c), 300/4 =
75 (nC/cm)2. In (d) 600/9 = 67 (nC/cm)2. In (e) 900/9 = 100 (nC/cm)2. The ranking is then a = e >
b = c > d.
(ii) We compute qA/r2 in each case. In (a) it is...