Call Now to Set Up Tutoring:

(888) 888-0446

AP Physics C Electricity : Calculating Electric Potential

Study concepts, example questions & explanations for AP Physics C Electricity

Create An Account

All AP Physics C Electricity Resources

1 Diagnostic Test 46 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 Next →

Example Question #1 : Calculating Electric Potential

A proton moves in a straight line for a distance of . Along this path, the electric field is uniform with a value of $2*10^7 \frac{V}{m}$ . Find the potential difference created by the movement.

The charge of a proton is $1.61*10^{-19}\text{C}$ .

Possible Answers:

1*10^9V

1*10^7V

$1*10^{10}V$

1*10^8V

Correct answer:

1*10^8V

Explanation:

Potential difference is given by the change in voltage

$V_a-V_b=\frac{W}{q}$

Work done by an electric field is equal to the product of the electric force and the distance travelled. Electric force is equal to the product of the charge and the electric field strength.

$\frac{W}{q}=\frac{Fd}{q}=\frac{qEd}{q}=Ed$

The charges cancel, and we are able to solve for the potential difference.

$\Delta V=Ed=(2*10^7\frac{V}{m})(5m)=1*10^8V$

Report an Error

Example Question #1 : Calculating Electric Potential

For a ring of charge with radius and total charge , the potential is given by $V=\frac{1}{4\pi\epsilon_0}\frac{q}{\sqrt{x^2+a^2}}$ .

Find the expression for electric field produced by the ring.

Possible Answers:

$\frac{1}{4\pi\epsilon_0}\frac{q}{(x^2+a^2)^{3/2}}}$

$\frac{1}{4\pi\epsilon_0}\frac{qx}{(x^2+a^2)^{1/2}}}$

$\frac{1}{4\pi\epsilon_0}\frac{q}{(x^2+a^2)^{1/2}}}$

$\frac{1}{4\pi\epsilon_0}\frac{qx}{(x^2+a^2)^{3/2}}}$

Correct answer:

$\frac{1}{4\pi\epsilon_0}\frac{qx}{(x^2+a^2)^{3/2}}}$

Explanation:

We know that $E=-\frac{dV}{dx}$ .

Using the given formula, we can find the electric potential expression for the ring.

$E=-\frac{d}{dx}(\frac{1}{4\pi\epsilon_0}\frac{q}{\sqrt{x^2+a^2}})$

Take the derivative and simplify.

$E=-(\frac{q}{4\pi\epsilon_0}\frac{1}{(x^2+a^2)^{3/2}}*-\frac{1}{2}*2x)=\frac{1}{4\pi\epsilon_0}\frac{qx}{(x^2+a^2)^{3/2}}$

Report an Error

Example Question #1 : Calculating Electric Potential

The potential outside of a charged conducting cylinder with radius and charge per unit length is given by the below equation.

$V=\frac{l}{2\pi\epsilon_0}ln\frac{R}{r}$

What is the electric field at a point located at a distance from the surface of the cylinder?

Possible Answers:

$\frac{l}{2\pi\epsilon_0r^3 }$

$\frac{l}{2\pi\epsilon_0r^2}$

$\frac{l}{2\pi\epsilon_0r}$

$\frac{lr}{2\pi \epsilon_0}$

Correct answer:

$\frac{l}{2\pi\epsilon_0r}$

Explanation:

The radial electric field outside the cylinder can be found using the equation $E_r=-\frac{dV}{dr}$ .

Using the formula given in the question, we can expand this equation.

$E_r=-\frac{dV}{dr}=-\frac{d}{dr}(\frac{l}{2\pi\epsilon_0}(lnR-lnr))$

Now, we can take the derivative and simplify.

$E_r=-\frac{1}{2\pi \epsilon_0}(\frac{1}{R}-\frac{1}{r})$

$E_r=-(-\frac{l}{2\pi\epsilon_0r})=\frac{l}{2\pi\epsilon_0r}$

Report an Error

Example Question #1 : Calculating Electric Potential

A proton moves in a straight line for a distance of . Along this path, the electric field is uniform with a value of $2*10^7 \frac{V}{m}$ . Find the work done on the proton by the electric field.

The charge of a proton is $1.61*10^{-19}\text{C}$ .

Possible Answers:

$6.44*10^{-11}J$

$0.8*10^{-11}J$

$3.22*10^{-11}J$

$1.61*10^{-11}J$

Correct answer:

$1.61*10^{-11}J$

Explanation:

Work done by an electric field is given by the product of the charge of the particle, the electric field strength, and the distance travelled.

W=qEd

We are given the charge ( $1.61*10^{-19}\text{C}$ ), the distance (), and the field strength ( $2*10^7 \frac{V}{m}$ ), allowing us to calculate the work.

$W=(1.61*10^{-19}C)(2*10^{7}\frac{V}{m})(5m)$

$W=(3.22*10^{-12}\frac{J}{m})(5m)$

$W=1.61*10^{-11}J$

Report an Error

Example Question #1 : Calculating Electric Potential

A negative charge of magnitude $9.0 \mu C$ is placed in a uniform electric field of $3.0 * 10^4 \frac{N}{C}$ , directed upwards. If the charge is moved 1.0m upwards, how much work is done on the charge by the electric field in this process?

Possible Answers:

$3.0 * 10^{-13} J$

$-3.3 * 10^{-6}J$

$-3.0 * 10^{-13} J$

$-2.7 * 10^{-4}J$

$2.7 * 10^{4}J$

Correct answer:

$-2.7 * 10^{-4}J$

Explanation:

Relevant equations:

$\Delta V = E * d$

$W = q \Delta V$

Given:

$E = 3.0 * 10^4 \frac{N}{C}$

d = 1.0 m

$q = -9.0 \mu C = -9.0 * 10 ^ {-9}C$

First, find the potential difference between the initial and final positions:

$\Delta V = (3.0 * 10^4 \frac{N}{C})(1.0m)= 3.0 * 10^4 \frac{N\cdot m}{C}$

2. Plug this potential difference into the work equation to solve for W:

$W = (-9.0 * 10^{-9}C)(3.0 * 10^4 \frac{N\cdot m}{C})$

$W = -2.7 * 10^{-4}J$

Report an Error

Example Question #1 : Calculating Electric Potential

Three point charges are arranged around the origin, as shown.

Ps0_threechargepotential

$\begin{matrix} &\text{Charge} & \text{Location}\\ Q_1& +3C&(-2cm,0) \\ Q_2&-5C &(4cm,0) \\ Q_3&+1C & (0,5cm) \end{matrix}$

Calculate the total electric potential at the origin due to the three point charges.

$k=9*10^9\frac{Nm^2}{C^2}$

Possible Answers:

$1.05*10^{12}V$

$2.65*10^{12}V$

$3.41*10^{11}V$

$4.05*10^{11}V$

Correct answer:

$4.05*10^{11}V$

Explanation:

Electric potential is a scalar quantity given by the equation:

$V = \frac{kq_{i}}{r_{i}}$

To find the total potential at the origin due to the three charges, add the potentials of each charge.

$V_{total}= V_{1}+V_{2}+V_{3} = \frac{kQ_{1}}{r_{1}}+\frac{kQ_{2}}{r_{2}}+\frac{kQ_{3}}{r_{3}}$

$V_{total}=\frac{(9*10^9)(3C)}{0.02m}+\frac{(9*10^9)(-5C)}{0.04m}+\frac{(9*10^9)(1C)}{0.05m}$

$V_{total}=1.35*10^{12}V+(-1.125*10^{12}V)+1.8*10^{11}V$

$V_{total}=4.05*10^{11}V$

Report an Error

Example Question #1 : Calculating Electric Potential

Three identical point charges with $q=1\mu C$ are placed so that they form an equilateral triangle as shown in the figure. Find the electric potential at the center point (black dot) of that equilateral triangle, where this point is at a equal distance, d=3mm , away from the three charges.

3_charges

$k=8.99*10^9\frac{Nm^2}{C^2}$

Possible Answers:

8.99*10^6V

8.99*10^3V

7.25*10^5V

1.90*10^6V

5.43*10^8V

Correct answer:

8.99*10^6V

Explanation:

The electric potential from point charges is $V=\frac{kq}{d}$ .

Knowing that all three charges are identical, and knowing that the center point at which we are calculating the electric potential is equal distance from the charges, we can multiply the electric potential equation by three.

$V=3\frac{kq}{d}$

Plug in the given values and solve for .

$V=3\frac{(8.99*10^9\ \frac{\text{Nm}^2}{\text{C}^2})(1* 10^{-6}\ \text{C})}{3*10^{-3}\ \text{m}}$

$V=8.99* 10^6\ \text{V}$

Report an Error

Example Question #1 : Calculating Electric Potential

Ap physics c e m potential problems 2 6 16 1

Eight point charges of equal magnitude are located at the vertices of a cube of side length . Calculate the potential at the center of the cube.

Possible Answers:

$\frac{\sqrt{3}Q}{6\pi\epsilon_0a}$

$\frac{8Q}{3\pi\epsilon_0a}$

$\frac{2\sqrt{2}Q}{\pi\epsilon_0a}$

$\frac{2Q}{\pi\epsilon_0a\sqrt{3}}$

$\frac{4Q}{\pi\epsilon_0a\sqrt{3}}$

Correct answer:

$\frac{4Q}{\pi\epsilon_0a\sqrt{3}}$

Explanation:

By the Pythagorean theorem, each charge is a distance

$d = \sqrt{\left (\frac{a}{2} \right )^2 + \left (\frac{a}{2} \right )^2+\left (\frac{a}{2} \right )^2} = \frac{\sqrt{3}}{2}a$

from the center of the cube, so the potential is

$V=8\times\left (\frac{Q}{4\pi\epsilon_0\left (\frac{\sqrt{3}}{2}a \right )} \right )$

$=\frac{4Q}{\pi\epsilon_0a\sqrt{3}}$

Report an Error

Example Question #1 : Calculating Electric Potential

Ap physics c e m potential problems 2 6 16 1 4

An infinite plane has a nonuniform charge density given by $\sigma(r)=\frac{qa}{2\pi(r^2+a^2)^{3/2}}$ . Calculate the potential at a distance above the origin.

You may wish to use the integral:

$\int\frac{x}{(x^2+a^2)^2}dx=\frac{1}{2a^2}\left(\frac{x^2}{x^2+a^2} \right )+C$

Possible Answers:

$\frac{q}{8\pi\epsilon_0a}$

$\frac{q}{2\pi\epsilon_0a}$

$\frac{q}{4\pi\epsilon_0a}$

$\frac{q}{16\pi\epsilon_0a}$

$\frac{q}{\pi\epsilon_0a}$

Correct answer:

$\frac{q}{8\pi\epsilon_0a}$

Explanation:

Use polar coordinates with the given surface charge density, $\sigma(r)=\frac{qa}{2\pi(r^2+a^2)^{3/2}}$ and area element $rd\theta d\phi$ . Noting that a point from the origin is a distance $\sqrt{r^2+a^2}$ from the point of interest, we calculate the potential as follows, integrating with respect to from to $\infty$ .

$V=\frac{1}{4\pi\epsilon_0} \int_{0}^{2\pi} \int_{0}^{\infty}\left (\frac{qa}{2\pi(r^2+a^2)^{3/2}} \right ) \frac{rdrd\theta}{\sqrt{r^2+a^2}}$

$=\frac{1}{4\pi\epsilon_0} (2\pi) \left(\frac{qa}{2\pi} \right )\int_{0}^{\infty}\left (\frac{1}{(r^2+a^2)^{3/2}} \right ) \frac{rdr}{\sqrt{r^2+a^2}}$

$=\frac{qa}{4\pi\epsilon_0} \int_{0}^{\infty}\frac{r}{(r^2+a^2)^2} dr$

$=\frac{qa}{4\pi\epsilon_0} \left [\frac{1}{2a^2}\left (\frac{x^2}{x^2+a^2} \right ) \right ]_{0}^{\infty}$

$=\frac{q}{8\pi\epsilon_0a} (1-0)$ (by limit)

$=\frac{q}{8\pi\epsilon_0a}$

Remark: This is exactly the charge distribution that would be induced on an infinite sheet of (grounded) metal if a negative charge were held a distance above it.

Report an Error

Example Question #1 : Calculating Electric Potential

Ap physics c e m potential problems 2 6 16 1 3

A nonuniformly charged hemispherical shell of radius (shown above) has surface charge density $\sigma(\theta)=b\cos^3\theta$ . Calculate the potential at the center of the opening of the hemisphere (the origin).

Possible Answers:

$\frac{Rb}{2\epsilon_0}$

$\frac{3Rb}{8\epsilon_0}$

$\frac{Rb}{15\epsilon_0}$

$\frac{Rb}{8\epsilon_0}$

$\frac{Rb}{3\epsilon_0}$

Correct answer:

$\frac{Rb}{8\epsilon_0}$

Explanation:

Use spherical coordinates with the given surface charge density $\sigma(\theta)=b\cos^3\theta$ , and area element $R^2\sin\theta d\theta d\phi$ . Every point on the hemispherical shell is a distance from the origin, so we calculate the potential as follows, noting the limits of integration for $\theta$ range from to $\pi/2$ .

$V=\frac{1}{4\pi\epsilon_0}\int_{0}^{2\pi}\int_{0}^{\pi/2}(b\cos^3\theta)\left (\frac{1}{R} \right )R^2\sin\theta d\theta d\phi$

$=\frac{Rb}{4\pi\epsilon_0} (2\pi) \int_{0}^{\pi/2}\cos^3\theta\sin\theta d\theta$

$=\frac{Rb}{2\epsilon_0} \left[\frac{-\cos^4\theta}{4} \right]_{0}^{\pi/2}$

$=\frac{Rb}{8\epsilon_0}$

Report an Error

← Previous 1 2 Next →

View Tutors

Aidan
Certified Tutor

Case Western Reserve University, Electrical Engineer, Electrical Engineering.

View Tutors

Dossevi
Certified Tutor

cole Ste Genevive Versailles, Bachelor of Science, Mathematics. Institut National Polytechnique de Grenoble, Master of Scienc...

View Tutors

Gregory
Certified Tutor

Pennsylvania State University-Main Campus, Bachelor of Science, Chemical Engineering. Carnegie Mellon University, Doctor of P...

All AP Physics C Electricity Resources

1 Diagnostic Test 46 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Reading Tutors in New York City, GMAT Tutors in San Diego, GRE Tutors in Denver, Biology Tutors in Phoenix, Math Tutors in Boston, Biology Tutors in Chicago, French Tutors in San Diego, French Tutors in Denver, Statistics Tutors in Denver, Chemistry Tutors in Philadelphia

Popular Courses & Classes

GRE Courses & Classes in Chicago, GMAT Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in New York City, Spanish Courses & Classes in Chicago, GMAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Washington DC, GRE Courses & Classes in Phoenix, Spanish Courses & Classes in Boston, GMAT Courses & Classes in Phoenix

Popular Test Prep

GMAT Test Prep in Los Angeles, SAT Test Prep in Washington DC, LSAT Test Prep in Los Angeles, SSAT Test Prep in Washington DC, ACT Test Prep in New York City, SSAT Test Prep in Phoenix, LSAT Test Prep in New York City, LSAT Test Prep in Washington DC, GMAT Test Prep in Houston, GRE Test Prep in Phoenix

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

AP Physics C Electricity : Calculating Electric Potential

Study concepts, example questions & explanations for AP Physics C Electricity

All AP Physics C Electricity Resources

Example Questions

Example Question #1 : Calculating Electric Potential

Example Question #1 : Calculating Electric Potential

Example Question #1 : Calculating Electric Potential

Example Question #1 : Calculating Electric Potential

Example Question #1 : Calculating Electric Potential

Example Question #1 : Calculating Electric Potential

Example Question #1 : Calculating Electric Potential

Example Question #1 : Calculating Electric Potential

Example Question #1 : Calculating Electric Potential

Example Question #1 : Calculating Electric Potential

All AP Physics C Electricity Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: