### Concept Items

#### 18.1 Electrical Charges, Conservation of Charge, and Transfer of Charge

- Most objects are neutral.
- Most objects have positive charge only.
- Most objects have negative charge only.
- Most objects have excess protons.

- No, an insulator cannot charge a conductor by induction.
- No, an insulating material cannot charge a conductor.
- Yes, an uncharged insulator can charge a conductor by induction.
- Yes, a charged insulator can charge a conductor upon contact.

True or false—A liquid can be an insulating material.

- true
- false

#### 18.1 Electrical Charges, Conservation of Charge, and Transfer of Charge

If you dive into a pool of seawater through which an equal amount of positively and negatively charged particles is moving, will you receive an electric shock?

- Yes, because negatively charged particles are moving.
- No, because positively charged particles are moving.
- Yes, because positively and negatively charged particles are moving.
- No, because equal amounts of positively and negatively charged particles are moving.

True or false—The high-voltage wires that you see connected to tall metal-frame towers are held aloft by insulating connectors, and these wires are wrapped in an insulating material.

- true
- false

By considering the molecules of an insulator, explain how an insulator can be overall neutral but carry a surface charge when polarized.

- Inside the insulator, the oppositely charged ends of the molecules cancel each other.
- Inside the insulator, the oppositely charged ends of the molecules do not cancel each other.
- The electron distribution in all the molecules shifts in every possible direction, leaving an excess of positive charge on the opposite end of each molecule.
- The electron distribution in all the molecules shifts in a given direction, leaving an excess of negative charge on the opposite end of each molecule.

#### 18.1 Electrical Charges, Conservation of Charge, and Transfer of Charge

A dust particle acquires a charge of −13 nC. How many excess electrons does it carry?

- 20.8 × 10
^{−28}electrons - 20.8 ×
^{−19}electrons - 8.1 × 10
^{10}electrons - 8.1 × 10
^{19}electrons

Two identical conducting spheres are charged with a net charge of +5.0 *q* on the first sphere and a net charge of −8.0 *q* on the second sphere. The spheres are brought together, allowed to touch, and then separated. What is the net charge on each sphere now?

- −3.0
*q* - −1.5
*q* - +1.5
*q* - +3.0
*q*

#### 18.2 Coulomb's Law

Two plastic spheres with uniform charge repel each other with a force of 10 N . If you remove the charge from one sphere, what will be the force between the spheres?

- The force will be 15 N.
- The force will be 10 N.
- The force will be 5 N.
- The force will be zero.

What creates a greater magnitude of force, two charges +*q* a distance r apart or two charges – *q* the same distance apart?

- Two charges +
*q*a distance*r*away - Two charges −
*q*a distance*r*away - The magnitudes of forces are equal.

In Newton’s law of universal gravitation, the force between two masses is proportional to the product of the two masses. What plays the role of mass in Coulomb’s law?

- the electric charge
- the electric dipole
- the electric monopole
- the electric quadruple

In terms of Coulomb’s law, why are water molecules attracted by positive and negative

charges?

- Water molecules are neutral.
- Water molecules have a third type of charge that is attracted by positive as well as negative charges.
- Water molecules are polar.
- Water molecule have either an excess of electrons or an excess of protons.

- The area of the cloud that was struck by lightning had a positive charge.
- The area of the cloud that was struck by lightning had a negative charge.
- The area of the cloud that was struck by lightning is neutral.
- The area of the cloud that was struck by lightning had a third type of charge.

Two particles with equal charge experience a force of 10 nN when they are 30 cm apart. What is the magnitude of the charge on each particle?

- −5.8 × 10
^{−10}C - −3.2 × 10
^{−10}C - +3.2 × 10
^{−10}C - +1.4 × 10
^{−5}C

Three charges are on a line. The left charge is *q*_{1} = 2.0 nC . The middle charge is *q*_{2} = 5.0 nC . The right charge is *q*_{3} = − 3.0 nC . The left and right charges are 2.0 cm from the middle charge. What is the force on the middle charge?

- −5.6 × 10
^{−4}N to the left - −1.12 × 10
^{−4}N to the left - +1.12 × 10
^{−4}N to the right - 5.6 × 10
^{−4}N to the right

#### 18.3 Electric Field

Why can electric fields not cross each other?

- Many electric-field lines can exist at any given point in space.
- No electric-field lines can exist at any given point in space.
- Only a single electric-field line can exist at any given point in space.
- Two electric-field lines can exist at the same point in space.

A constant electric field is (4.5 × 10^{5} N/C)*ŷ*. In which direction is the force on a −20 nC charge placed in this field?

- The direction of the force is in the $+\widehat{x}$ direction.
- The direction of the force is in the $+\widehat{x}$ direction.
- The direction of the force is in the −ŷ direction.
- The direction of the force is in the +ŷ direction.

An arbitrary electric field passes through a box-shaped volume. There are no charges in the box. If 11 electric-field lines enter the box, how many electric-field lines must exit the box?

- nine electric field lines
- 10 electric field lines
- 11 electric field lines
- 12 electric field lines

In a science-fiction movie, a villain emits a radial electric field to repulse the hero. Knowing that the hero is electrically neutral, is this possible? Explain your reasoning.

- No, because an electrically neutral body cannot be repelled or attracted.
- No, because an electrically neutral body can be attracted but not repelled.
- Yes, because an electrically neutral body can be repelled or attracted.
- Yes, because an electrically neutral body can be repelled.

An electric field (15 N/C)*ẑ* applies a force (− 3 × 10^{–6} N)*ẑ* on a particle. What is the charge on the particle?

- −2.0 × 10
^{–7}C - 2.0 × 10
^{–7}C - 2.0 × 10
^{–8}C - 2.0 × 10
^{–9}C

Two uniform electric fields are superimposed. The first electric field is ${\overrightarrow{\text{E}}}_{\text{1}}\text{=(14}\text{N/C)}\widehat{x}$ . The second electric field is ${\overrightarrow{\text{E}}}_{\text{2}}\text{=(7}\text{.0N/C)}\u0177$ . With respect to the positive *x* axis, at which angle will a positive test charge accelerate in this combined field?

- 27°
- 54°
- 90°
- 108°

#### 18.4 Electric Potential

True or false—The potential from a group of charges is the sum of the potentials from each individual charge.

- false
- true

True or false—The characteristics of an electric field make it analogous to the gravitational field near the surface of Earth.

- false
- true

- It moves toward regions of higher potential because its charge is negative.
- It moves toward regions of lower potential because its charge is negative
- It moves toward regions of higher potential because its charge is positive.
- It moves toward regions of lower potential because its charge is positive.

What is the relationship between voltage and energy? More precisely, what is the relationship between potential difference and electric potential?

- Voltage is the energy per unit mass at some point in space.
- Voltage is the energy per unit length in space.
- Voltage is the energy per unit charge at some point in space.
- Voltage is the energy per unit area in space.

Three parallel plates are stacked above each other, with a separation between each plate. If the potential difference between the first two plates is ΔV_{1} and the potential between the second two plates is Δ*V*_{2} , what is the potential difference between the first and the third plates?

- Δ
*V*_{3}= Δ*V*_{2}+ Δ*V*_{1} - Δ
*V*_{3}= Δ*V*_{2}− Δ*V*_{1} - Δ
*V*_{3}= Δ*V*_{2}/ Δ*V*_{1} - Δ
*V*_{3}= Δ*V*_{2}×Δ*V*_{1}

You move a charge *q* from *r*_{i} = 20 cm to *r*_{f} = 40 cm from a fixed charge *Q* = 10 nC. What is the difference in potential for these two positions?

- −2.2 × 10
^{2}V - −1.7 × 10
^{3}V - −2.2 × 10
^{4}V - −1.7 × 10
^{2}V

How much work is required from an outside agent to move an electron from *x*_{i} = 0 to *x*_{f} = 20 cm in an electric field $(50\text{N/C})\widehat{x}$ ?

- 1.6 × 10
^{−15}J - 1.6 × 10
^{−16}J - 1.6 × 10
^{−20}J - 1.6 × 10
^{−18}J

#### 18.5 Capacitors and Dielectrics

You insert a dielectric into an air-filled capacitor. How does this affect the energy stored in the capacitor?

- Energy stored in the capacitor will remain same.
- Energy stored in the capacitor will decrease.
- Energy stored in the capacitor will increase.
- Energy stored in the capacitor will increase first, and then it will decrease.

True or false— Placing a dielectric between the plates of a capacitor increases the energy of the capacitor.

- false
- true

True or false— The electric field in an air-filled capacitor is reduced when a dielectric is inserted between the plates.

- false
- true

### Critical Thinking Items

#### 18.5 Capacitors and Dielectrics

When you insert a dielectric into a capacitor, the energy stored in the capacitor decreases. If you take the dielectric out, the energy increases again. Where does this energy go in the former case, and where does the energy come from in the latter case?

- Energy is utilized to remove the dielectric and is released when the dielectric is introduced between the plates.
- Energy is released when the dielectric is added and is utilized when the dielectric is introduced between the plates.
- Energy is utilized to polarize the dielectric and is released when the dielectric is introduced between the plates.
- Energy is released to polarize the dielectric and is utilized when dielectric is introduced between the plates.

### Problems

#### 18.5 Capacitors and Dielectrics

A 4.12 *µ*F parallel-plate capacitor has a plate area of 2,000 cm^{2} and a plate separation of 10 *µ*m . What dielectric is between the plates?

- 1, the dielectric is strontium titanate
- 466, the dielectric is strontium
- 699, the dielectric is strontium nitrate
- 1,000, the dielectric is strontium chloride

- $$C=\frac{R}{k}$$
- $$C=\frac{k}{R}$$
- $$C=\frac{V}{Q}$$
- $$C=QV$$

### Performance Task

#### 18.5 Capacitors and Dielectrics

Newton’s law of universal gravitation is

where $G=6.67\phantom{\rule{0.25em}{0ex}}\times \phantom{\rule{0.25em}{0ex}}{10}^{-11}\text{\hspace{0.17em}}{\text{m}}^{3}\text{/kg}\cdot {\text{s}}^{2}$. This describes the gravitational force between two point masses *m*_{1} and *m*_{2}.

Coulomb’s law is

where $k=8.99\phantom{\rule{0.25em}{0ex}}\times \phantom{\rule{0.25em}{0ex}}{10}^{9}\text{\hspace{0.17em}}\text{N}\cdot {\text{m}}^{\text{2}}{\text{/C}}^{\text{2}}$. This describes the electric force between two point charges *q*_{1} and *q*_{2}.

(a) Describe how the force in each case depends on the distance *r* between the objects. How do the forces change if the distance is reduced by half? If the distance is doubled?

(b) Describe the similarities and differences between the two laws. Consider the signs of the quantities that create the interaction (i.e., mass and charge), the constants *G* and *k*, and their dependence on separation *r*.

(c) Given that the electric force is much stronger than the gravitational force, discuss why the law for gravitational force was discovered much earlier than the law for electric force.

(d) Consider a hydrogen atom, which is a single proton orbited by a single electron. The electric force holds the electron and proton together so that the hydrogen atom has a radius of about $0.5\phantom{\rule{0.25em}{0ex}}\times \phantom{\rule{0.25em}{0ex}}{10}^{\mathrm{-10}}\text{\hspace{0.17em}}\text{m}$. Assuming the force between electron and proton does not change, what would be the approximate radius of the hydrogen atom if $k=6.67\phantom{\rule{0.25em}{0ex}}\times \phantom{\rule{0.25em}{0ex}}{10}^{\mathrm{-11}}\text{\hspace{0.17em}}\text{N}\cdot {\text{m}}^{\text{2}}{\text{/C}}^{\text{2}}$?