## 19.1 Electric Potential Energy: Potential Difference

An electron is placed in an electric field of 12.0 N/C to the right. What is the resulting force on the electron?

- 1.33×10
^{-20}N right - 1.33×10
^{-20}N left - 1.92×10
^{-18}N right - 1.92×10
^{-18}N left

A positively charged object in a certain electric field is currently being pushed west by the resulting force. How will the force change if the charge grows? What if it becomes negative?

A −5.0 C charge is being forced south by a 60 N force. What are the magnitude and direction of the local electric field?

- 12 N/C south
- 12 N/C north
- 300 N/C south
- 300 N/C north

A charged object has a net force of 100 N east acting on it due to an electric field of 50 N/C pointing north. How is this possible? If not, why not?

How many electrons have to be moved by a car battery containing 7.20×10^{5 }J at 12 V to reduce the energy by 1%?

- 4.80×10
^{27} - 4.00×10
^{26} - 3.75×10
^{21} - 3.13×10
^{20}

Most of the electricity in the power grid is generated by powerful turbines spinning around. Why don’t these turbines slow down from the work they do moving electrons?

A typical AAA battery can move 2000 C of charge at 1.5 V. How long will this run a 50 mW LED?

- 1000 minutes
- 120,000 seconds
- 15 hours
- 250 minutes

Find an example car (or other vehicle) battery, and compute how many of the AAA batteries in the previous problem it would take to equal the energy stored in it. Which is more compact?

What is the internal energy of a system consisting of two point charges, one 2.0 µC, and the other −3.0 µC, placed 1.2 m away from each other?

- −3.8×10
^{-2}J - −4.5×10
^{-2}J - 4.5×10
^{-2}J - 3.8×10
^{-2}J

A system of three point charges has a 1.00 µC charge at the origin, a −2.00 µC charge at *x*=30 cm, and a 3.00 µC charge at *x*=70 cm. What is the total stored potential energy of this configuration?

A system has 2.00 µC charges at (50 cm, 0) and (−50 cm, 0) and a −1.00 µC charge at (0, 70 cm). As the *y*-coordinate of the −1.00 µC charge increases, the potential energy ___. As the *y*-coordinate of the −1.00 µC charge decreases, the potential energy ___.

- increases, increases
- increases, decreases
- decreases, increases
- decreases, decreases

A system of three point charges has a 1.00 µC charge at the origin, a −2.00 µC charge at *x*=30 cm, and a 3.00 µC charge at *x*=70 cm. What happens to the total potential energy of this system if the −2.00 µC charge and the 3.00 µC charge trade places?

Take a square configuration of point charges, two positive and two negative, all of the same magnitude, with like charges sharing diagonals. What will happen to the internal energy of this system if one of the negative charges becomes a positive charge of the same magnitude?

- increase
- decrease
- no change
- not enough information

Take a square configuration of point charges, two positive and two negative, all of the same magnitude, with like charges sharing diagonals. What will happen to the internal energy of this system if the sides of the square decrease in length?

A system has 2.00 µC charges at (50 cm, 0) and (−50 cm, 0) and a −1.00 µC charge at (0, 70 cm), with a velocity in the –*y*-direction. When the −1.00 µC charge is at (0, 0) the potential energy is at a ___ and the kinetic energy is ___.

- maximum, maximum
- maximum, minimum
- minimum, maximum
- minimum, minimum

What is the velocity of an electron that goes through a 10 V potential after initially being at rest?

## 19.2 Electric Potential in a Uniform Electric Field

A negatively charged massive particle is dropped from above the two plates in Figure 19.5 into the space between them. Which best describes the trajectory it takes?

- A rightward-curving parabola
- A leftward-curving parabola
- A rightward-curving section of a circle
- A leftward-curving section of a circle

Two massive particles with identical charge are launched into the uniform field between two plates from the same launch point with the same velocity. They both impact the positively charged plate, but the second one does so four times as far as the first. What sign is the charge? What physical difference would give them different impact points (quantify as a relative percent)? How does this compare to the gravitational projectile motion case?

Two plates are lying horizontally, but stacked with one 10.0 cm above the other. If the upper plate is held at +100 V, what is the magnitude and direction of the electric field between the plates if the lower is held at +50.0 V? -50.0 V?

- 500 V/m, 1500 V/m, down
- 500 V/m, 1500 V/m, up
- 1500 V/m, 500 V/m, down
- 1500 V/m, 500 V/m, up

Two parallel conducting plates are 15 cm apart, each with an area of 0.75 m^{2}. The left one has a charge of -0.225 C placed on it, while the right has a charge of 0.225 C. What is the magnitude and direction of the electric field between the two?

Consider three parallel conducting plates, with a space of 3.0 cm between them. The leftmost one is at a potential of +45 V, the middle one is held at ground, and the rightmost is at a potential of -75 V. What is the magnitude of the average electric field on an electron traveling between the plates? (Assume that the middle one has holes for the electron to go through.)

- 1500 V/m
- 2500 V/m
- 4000 V/m
- 2000 V/m

A new kind of electron gun has a rear plate at −25.0 kV, a grounded plate 2.00 cm in front of that, and a +25.0 kV plate 4.00 cm in front of that. What is the magnitude of the average electric field?

A certain electric potential isoline graph has isolines every 5.0 V. If six of these lines cross a 40 cm path drawn between two points of interest, what is the (magnitude of the average) electric field along this path?

- 750 V/m
- 150 V/m
- 38 V/m
- 75 V/m

Given a system of two parallel conducting plates held at a fixed potential difference, describe what happens to the isolines of the electric potential between them as the distance between them is changed. How does this relate to the electric field strength?

## 19.4 Equipotential Lines

How would Figure 19.10 be different with two positive charges replacing the two negative charges?

- The equipotential lines would have positive values.
- It would actually resemble Figure 19.9.
- no change
- not enough information

Consider two conducting plates, placed on adjacent sides of a square, but with a 1-m space between the corner of the square and the plate. These plates are not touching, not centered on each other, but are at right angles. Each plate is 1 m wide. If the plates are held at a fixed potential difference Δ*V*, draw the equipotential lines for this system.

As isolines of electric potential get closer together, the electric field gets stronger. What shape would a hill have as the isolines of gravitational potential get closer together?

- constant slope
- steeper slope
- shallower slope
- a U-shape

Between Figure 19.9 and Figure 19.10, which more closely resembles the gravitational field between two equal masses, and why?

How much work is necessary to keep a positive point charge in orbit around a negative point charge?

- A lot; this system is unstable.
- Just a little; the isolines are far enough apart that crossing them doesn’t take much work.
- None; we’re traveling along an isoline, which requires no work.
- There’s not enough information to tell.

Consider two conducting plates, placed on adjacent sides of a square, but with a 1-m space between the corner of the square and the plate. These plates are not touching, not centered on each other, but are at right angles. Each plate is 1 m wide. If the plates are held at a fixed potential difference Δ*V*, sketch the path of both a positively charged object placed between the near ends, and a negatively charged object placed near the open ends.

## 19.5 Capacitors and Dielectrics

Two parallel plate capacitors are otherwise identical, except the second one has twice the distance between the plates of the first. If placed in otherwise identical circuits, how much charge will the second plate have on it compared to the first?

- four times as much
- twice as much
- the same
- half as much

In a very simple circuit consisting of a battery and a capacitor with an adjustable distance between the plates, how does the voltage vary as the distance is altered?

A parallel plate capacitor with adjustable-size square plates is placed in a circuit. How does the charge on the capacitor change as the length of the sides of the plates is increased?

- it grows proportional to length
^{2} - it grows proportional to length
- it shrinks proportional to length
- it shrinks proportional to length
^{2}

Design an experiment to test the relative permittivities of various materials, and briefly describe some basic features of the results.

A student was changing one of the dimensions of a square parallel plate capacitor and measuring the resultant charge in a circuit with a battery. However, the student forgot which dimension was being varied, and didn’t write it or any units down. Given the table, which dimension was it?

Dimension | Charge(µC) |

1.00 | 0.50 |

1.10 | 0.61 |

1.20 | 0.71 |

1.30 | 0.86 |

- The distance between the plates
- The area
- The length of a side
- Both the area and the length of a side

In an experiment in which a circular parallel plate capacitor in a circuit with a battery has the radius and plate separation grow at the same relative rate, what will happen to the total charge on the capacitor?

## 19.7 Energy Stored in Capacitors

Consider a parallel plate capacitor, with no dielectric material, attached to a battery with a fixed voltage. What happens when a dielectric is inserted into the capacitor?

- Nothing changes, except now there is a dielectric in the capacitor.
- The energy in the system decreases, making it very easy to move the dielectric in.
- You have to do work to move the dielectric, increasing the energy in the system.
- The reversed polarity destroys the battery.

Consider a parallel plate capacitor with no dielectric material. It was attached to a battery with a fixed voltage to charge up, but now the battery has been disconnected. What happens to the energy of the system and the dielectric material when a dielectric is inserted into the capacitor?

What happens to the energy stored in a circuit as you increase the number of capacitors connected in parallel? Series?

- increases, increases
- increases, decreases
- decreases, increases
- decreases, decreases

What would the capacitance of a capacitor with the same total internal energy as the car battery in Example 19.1 have to be? Can you explain why we use batteries instead of capacitors for this application?

Consider a parallel plate capacitor with metal plates, each of square shape of 1.00 m on a side, separated by 1.00 mm. What is the energy of this capacitor with 3.00×10^{3} V applied to it?

- 3.98×10
^{-2}J - 5.08×10
^{14}J - 1.33×10
^{-5}J - 1.69×10
^{11}J

Consider a parallel plate capacitor with metal plates, each of square shape of 1.00 m on a side, separated by 1.00 mm. What is the internal energy stored in this system if the charge on the capacitor is 30.0 µC?

Consider a parallel plate capacitor with metal plates, each of square shape of 1.00 m on a side, separated by 1.00 mm. If the plates grow in area while the voltage is held fixed, the capacitance ___ and the stored energy ___.

- decreases, decreases
- decreases, increases
- increases, decreases
- increases, increases

Consider a parallel plate capacitor with metal plates, each of square shape of 1.00 m on a side, separated by 1.00 mm. What happens to the energy of this system if the area of the plates increases while the charge remains fixed?