Question

1. Three identical point charges, each of charge q are located at the vertices of an equilateral triangle as in figure below. The distance from the center of the triangle to each vertex is a . a. Show that the electric field at the center of the triangle is zero. b. Find a symbolic expression for the electric potential at the center of the triangle. c. Give a physical explanation of the fact that the electric potential is not zero, yet the electric field is zero at the center. 

          1. Three identical point charges, each of charge q are located at the vertices of an equilateral triangle as in figure below. The distance from the center of the triangle to each vertex is a .
a. Show that the electric field at the center of the triangle is zero.
b. Find a symbolic expression for the electric potential at the center of the triangle.
c. Give a physical explanation of the fact that the electric potential is not zero, yet the electric field is zero at the center.
Show more…
1. Three identical point charges, each of charge q are located at the vertices of an equilateral triangle as in figure below. The distance from the center of the triangle to each vertex is a . a. Show that the electric field at the center of the triangle is zero. b. Find a symbolic expression for the electric potential at the center of the triangle. c. Give a physical explanation of the fact that the electric potential is not zero, yet the electric field is zero at the center.

Added by Brittany P.

Close

University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
Three identical point charges, each of charge q are located at the vertices of an equilateral triangle as in figure below. The distance from the center of the triangle to each vertex is a. a. Show that the electric field at the center of the triangle is zero. b. Find a symbolic expression for the electric potential at the center of the triangle. c. Give a physical explanation of the fact that the electric potential is not zero, yet the electric field is zero at the center.
Close icon
Play audio
Feedback
Powered by NumerAI
Ivan Kochetkov Danielle Fairburn
Jennifer Stoner verified

Vishal Gupta and 99 other subject Physics 101 Mechanics educators are ready to help you.

Ask a new question
*

Labs

-

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs
*

Key Concepts

-
Key Concept
Premium Feature
Explore the core concept behind this problem.
Play button
Key Concept
Premium Feature
Explore the core concept behind this problem.
Your browser does not support the video tag.
*

Recommended Videos

-
three-identical-point-charges-each-of-charge-q-are-located-at-the-vertices-of-an-equilateral-triangl

Three identical point charges each of charge $q$ are located at the vertices of an equilateral triangle as in Figure $\mathrm{P} 16.16$ . The distance from the center of the triangle to each vertex is a. (a) Show that the electric field at the center of the triangle is zero. (b) Find a symbolic expression for the electric potential at the center of the triangle. (c) Give a physical explanation of the fact that the electric potential is not zero, yet the electric field is zero at the center.

College Physics

three-identical-point-charges-each-of-charge-are-located-at-the-vertices-of-an-equilateral-triangle-as-in-the-figure-shown-below_-the-distance-from-the-center-of-the-triangle-to-each-vertex-84363

Three identical point charges, each of charge q, are located at the vertices of an equilateral triangle as shown in the figure below. The distance from the center of the triangle to each vertex is r. (a) Show that the electric field at the center of the triangle is zero. (b) Find a symbolic expression for the electric potential at the center of the triangle. (Use any variable or symbol stated above along with the following as necessary: Ke for Coulomb's constant) (c) Give a physical explanation of the fact that the electric potential is not zero, yet the electric field is zero at the center.

Vishal G.
three-equal-positive-charges-are-at-the-corners-of-an-equilateral-triangle-of-side-as-shown-in-the-figure-below-assume-the-three-charges-together-create-an-electric-field-po-find-the-locatio-48941

Three equal positive charges q are at the corners of an equilateral triangle of side a as shown in the figure below. Assume the three charges together create an electric field. (b) Find the location of one point (other than ∞) where the electric field is zero. at P at the center of the triangle at each vertex at the center of the base (c) What is the magnitude of the electric field at P due to the two charges at the base? (Use any variable or symbol stated above along with the following as necessary: ke.) E = √3 k q / a^2

Ivan K.
*

Recommended Textbooks

-
University Physics with Modern Physics

University Physics with Modern Physics

Hugh D. Young 14th Edition
achievement 1,271 solutions
Physics: Principles with Applications

Physics: Principles with Applications

Douglas C. Giancoli 7th Edition
achievement 1,903 solutions
Fundamentals of Physics

Fundamentals of Physics

David Halliday, Robert Resnick , Jearl Walker 10th Edition
achievement 1,210 solutions
*

Transcript

-
0:00 Hi.
00:01 Here in this given problem this is an equilateral triangle.
00:11 Let it be represented as a, b, c.
00:17 Three charges at the three vertices q each and the side of equilateral triangle that is given as a.
00:31 Then the center of this equilateral triangle, center which is the point.
00:37 Of intersection of the three medians of the equilateral triangle and we know these distances are each a -o is equal to b -o is equal to c -o and if we assume it to be r it is actually two -third of the length of the median of the equilateral triangle medium means this perpendicular bisector of any of the side of this triangle let this point to be d so this median means ad that will be given by because this angle will be 30 degree half of the vertex angle a vertex angle which is 60 degree so that is a b cost 60 degree sorry a b cost 30 degree means we can say this is a root 3 by 2.
01:50 So the distance of observation point o from each vertex that is 2 third of the length of the median means a root 3 by 2 canceling this 2 finally this is a root 3 by 3.
02:09 Now at the center of this triangle there are 3 electric fields as electric field goes away from the positive charge so this is e because of a then e because of b going like this away from b and e because of c going like this and all these three electric fields will be equal in magnitude ea is equal to e b is equal to e c and using the expression for electric field that is kq by r square means this is k q by for r that is a root 3 by 3 square so here it becomes 3 k q by a square now we can resolve e c and e b into components your horizontal components will cancel each other and vertical components in upward direction will be added and these components are ec, e b because this angle will be 60 degree for both so this is e b cost 60 degree plus e c cos 60 degree in upward direction and this so there are two elective fields now at this center one is e in downward direction e down which is equal to ea means 3k q by a square.
03:54 And in upward direction e up, that is e b, cost 60 degree plus ec cost 60 degree...
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Join the community

18,000,000+

Students on Numerade

Trusted by students at 8,000+ universities

Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever