College Physics: Reasoning and Relationships

Nicholas J. Giordano

Chapter 18

Electric Potential - all with Video Answers

Educators

Section 1

Electric Potential Energy

Problem 1

Two point particles of charge $Q_{1}=45 \mu \mathrm{C}$ and $Q_{2}=85 \mu \mathrm{C}$ are found to have a potential energy of
40 J. What is the distance between the charges?

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 2

Two particles with $Q_{1}=45 \mu \mathrm{C}$ and $Q_{2}=85 \mu \mathrm{C}$ are initially separated by a distance of $2.5 \mathrm{m}$ and then brought closer together so that the final separation is $1.5 \mathrm{m}$. What is the change in the
electric potential energy?

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 3

The nucleus of a helium atom contains two protons. In a simple model of this nucleus, the protons are viewed as point particles separated by $1.0 \mathrm{fm}\left(1.0 \times 10^{-15} \mathrm{m}\right) .$ What is the electric potential energy of the two protons?

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 4

Two point charges $Q_{1}=3.5 \mu \mathrm{C}$ and $Q_{2}=7.5 \mu \mathrm{C}$ are initially very far apart. They are then brought together, with a final separation of $2.5 \mathrm{m}$. How much work does it take to bring them together?

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 5

A simple model of a hydrogen atom pictures the electron and proton as point charges separated by $0.050 \mathrm{nm},$ and in Example 18.1 we calculated the associated electric potential energy. If the electron is initially at rest, how much work is required to "break apart" these two charges, that is, to separate them by a very large distance?

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 6

Consider an electric dipole consisting of charges $+Q$ and $-Q$ as sketched in Figure P18.6. How much work is required to place a charge $q$ at the origin? Assume $q$ starts from very far away.

Ajay Singhal

Numerade Educator

Problem 7

Two point charges are located as shown in Figure $\mathrm{P} 18.7,$ with charge $q_{1}=+2.5 \mathrm{C}$ at $x=-3.0 \mathrm{m}$
$y=0,$ and charge $q_{2}=+4.0 \mathrm{C}$ at $x=+1.0 \mathrm{m}, y=+2.0 \mathrm{m} .$ An electron is now taken from a point very far away and placed at the origin. How much work must be done on the electron to move it to the origin?

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 8

The electric field in a particular region of space is found to be uniform, with a magnitude of 400 N/C and parallel to the +y direction.
a. What is the change in electric potential energy of a charge $q=3.5 \mu \mathrm{C}$ if it is moved from $(x, y)=(20 \mathrm{cm}, 45 \mathrm{cm}) \mathrm{to}(5 \mathrm{cm}, 30 \mathrm{cm}) ?$
b. What is the change in electric potential energy if the charge is moved the same distance along the $x$ axis?

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 9

Three point charges $Q_{1}=2.5 \mu \mathrm{C}, Q_{2}=4.5 \mu \mathrm{C},$ and $Q_{3}=-3.5 \mu \mathrm{C}$ are arranged as shown in Figure $\mathrm{P} 18.9 .$ What is the total electric potential energy of this system?

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 10

Consider again the three charges in Figure $\mathrm{P} 18.9$ with $Q_{1}=2.5 \mu \mathrm{C}, Q_{2}=4.5 \mu \mathrm{C},$ and $Q_{3}=-3.5 \mu \mathrm{C} .$ A fourth charge $q=-5.0 \mu \mathrm{C}$ is brought from very far away and placed at the origin.
a. How much work is required in this process?
b. How much work is required to move $q$ from the origin to a distance that is very far away?

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 11

A proton is placed at the origin. An electron that is initially very far away is then taken on the path shown in Figure $\mathrm{P} 18.11$ and eventually stops a distance of $3.0 \mathrm{nm}\left(=3.0 \times 10^{-9} \mathrm{m}\right)$ from the proton. How much work was done on the electron to move it along this path?

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 12

An electron and a proton are a distance $r=7.5 \times 10^{-9} \mathrm{m}$ apart. How much energy is required to increase their separation by a factor of two?

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 13

Two point charges $Q_{1}=+1.2 \mu \mathrm{C}$ and $Q_{2}=+3.2 \mu \mathrm{C}$ are initially separated by $1.0 \mathrm{m}$ and held fixed. The charges are then released, and both move in response to the electric force between them. What is the sum of the kinetic energies of the two particles when they are very far apart?

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 14

The two electrons in a helium atom are separated by about 0.10 $\mathrm{nm}$ and the separation between either electron and the nucleus is about $0.050 \mathrm{nm}$. What is the total electric potential energy of the atom? Assume the nucleus is a point charge with $q=+2 e$ and for simplicity do not include the potential energy associated with the Coulomb repulsion of the two protons in the nucleus. Compare your answer with the ionization energy of a helium atom and with the energy required to remove both electrons from a helium atom.

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator

Problem 15

An oxygen ion $\mathrm{O}^{2-}$ is a distance $r=5.0 \times 10^{-10} \mathrm{m}$ from a $\mathrm{H}^{+}$ ion. How much energy is required to separate them completely? Treat both ions as point charges.

Varsha Aggarwal

Varsha Aggarwal

Numerade Educator