Homework Help is Here – Start Your Trial Now!
Science
Physics
Part 1: The Charged Semi-Circular Hoop A thin plastic rod is bent into the shape of a semicircle of radius a. It is charged negatively with -Q Coulombs of charge. Show how to derive the equation for the electric field at the origin of the coordinate axes in the following diagram. 8 dq 1. Identify the position vector for a small portion of the source charge distribution and express it in plane polar coordinates using a unit vector in those coordinates. 2. Identify the position vector for the field point and express your answer as Tp =. Recall, the field point is at the origin. 3. Determine an expression (in plane polar coordinates) for the vector R that points from the source to the field point. 4. Express dq in two ways. First in terms of a linear charge density λ and the integration variable. Then write it in terms of quantities given in the problem statement. Partial Answer: dq = Ads where ds is a differential element of arc-length and 2=%/cio (circumference of a half circle) 2 5. Write the expression (the integral) for E at the field point. Answer: E =k, Jax J = O ta fde

Part 1: The Charged Semi-Circular Hoop A thin plastic rod is bent into the shape of a semicircle of radius a. It is charged negatively with -Q Coulombs of charge. Show how to derive the equation for the electric field at the origin of the coordinate axes in the following diagram. 8 dq 1. Identify the position vector for a small portion of the source charge distribution and express it in plane polar coordinates using a unit vector in those coordinates. 2. Identify the position vector for the field point and express your answer as Tp =. Recall, the field point is at the origin. 3. Determine an expression (in plane polar coordinates) for the vector R that points from the source to the field point. 4. Express dq in two ways. First in terms of a linear charge density λ and the integration variable. Then write it in terms of quantities given in the problem statement. Partial Answer: dq = Ads where ds is a differential element of arc-length and 2=%/cio (circumference of a half circle) 2 5. Write the expression (the integral) for E at the field point. Answer: E =k, Jax J = O ta fde

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
See similar textbooks
icon
Related questions
Question

Question 5 please 

thank you 

Part 1: The Charged Semi-Circular Hoop A thin plastic rod is bent into the shape of a semicircle of radius a. It is charged negatively with -Q Coulombs of charge. Show how to derive the equation for the electric field at the origin of the coordinate axes in the following diagram. 8 1. Identify the position vector for a small portion of the source charge distribution and express it in plane polar coordinates using a unit vector in those coordinates. da 2. Identify the position vector for the field point and express your answer as 7 = <put your answer here>. Recall, the field point is at the origin. 3. Determine an expression (in plane polar coordinates) for the vector R that points from the source to the field point. 2=% circumferen 4. Express dq in two ways. First in terms of a linear charge density λ and the integration variable. Then write it in terms of quantities given in the problem statement. Partial Answer: dq = Ads where ds is a differential element of arc-length and nference of a half circle) 5. Write the expression (the integral) for E' at the field point. Answer: E = k₁, d0 f de 6. Convert the previous expression back into Cartesian coordinates. πα
Transcribed Image Text:Part 1: The Charged Semi-Circular Hoop A thin plastic rod is bent into the shape of a semicircle of radius a. It is charged negatively with -Q Coulombs of charge. Show how to derive the equation for the electric field at the origin of the coordinate axes in the following diagram. 8 1. Identify the position vector for a small portion of the source charge distribution and express it in plane polar coordinates using a unit vector in those coordinates. da 2. Identify the position vector for the field point and express your answer as 7 = <put your answer here>. Recall, the field point is at the origin. 3. Determine an expression (in plane polar coordinates) for the vector R that points from the source to the field point. 2=% circumferen 4. Express dq in two ways. First in terms of a linear charge density λ and the integration variable. Then write it in terms of quantities given in the problem statement. Partial Answer: dq = Ads where ds is a differential element of arc-length and nference of a half circle) 5. Write the expression (the integral) for E' at the field point. Answer: E = k₁, d0 f de 6. Convert the previous expression back into Cartesian coordinates. πα
Expert Solution
steps

Step by step

Solved in 4 steps with 5 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Weakly interacting gases
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON
SEE MORE TEXTBOOKS