Electrical Engineering (EE) Exam > Electrical Engineering (EE) Notes > Electromagnetic Fields Theory (EMFT) > PPT: Poisson’s & Laplace Equations
PPT: Poisson’s & Laplace Equations | Electromagnetic Fields Theory (EMFT) - Electrical Engineering (EE) PDF Download
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1 Poisson’s and Laplace Equations A useful approach to the calculation of electric potentials Relates potential to the charge density. The electric field is related to the charge density by the divergence relationship The electric field is related to the electric potential by a gradient relationship Therefore the potential is related to the charge density by Poisson's equation In a charge-free region of space, this becomes Laplace's equation Page 2 Poisson’s and Laplace Equations A useful approach to the calculation of electric potentials Relates potential to the charge density. The electric field is related to the charge density by the divergence relationship The electric field is related to the electric potential by a gradient relationship Therefore the potential is related to the charge density by Poisson's equation In a charge-free region of space, this becomes Laplace's equation Potential of a Uniform Sphere of Charge outside inside Page 3 Poisson’s and Laplace Equations A useful approach to the calculation of electric potentials Relates potential to the charge density. The electric field is related to the charge density by the divergence relationship The electric field is related to the electric potential by a gradient relationship Therefore the potential is related to the charge density by Poisson's equation In a charge-free region of space, this becomes Laplace's equation Potential of a Uniform Sphere of Charge outside inside Poisson’s and Laplace Equations Poisson’s Equation From the point form of Gaus's Law Del_dot_ D r v Definition D D eE and the gradient relationship E DelV - Del_D Del_ eE () Del_dot_ eDelV ( ) - r v Del_DelV r v - e Laplace’s Equation if r v 0 Del_dot_D r v Del_Del Laplacian The divergence of the gradient of a scalar function is called the Laplacian. Page 4 Poisson’s and Laplace Equations A useful approach to the calculation of electric potentials Relates potential to the charge density. The electric field is related to the charge density by the divergence relationship The electric field is related to the electric potential by a gradient relationship Therefore the potential is related to the charge density by Poisson's equation In a charge-free region of space, this becomes Laplace's equation Potential of a Uniform Sphere of Charge outside inside Poisson’s and Laplace Equations Poisson’s Equation From the point form of Gaus's Law Del_dot_ D r v Definition D D eE and the gradient relationship E DelV - Del_D Del_ eE () Del_dot_ eDelV ( ) - r v Del_DelV r v - e Laplace’s Equation if r v 0 Del_dot_D r v Del_Del Laplacian The divergence of the gradient of a scalar function is called the Laplacian. LapR xx Vxy , z , () d d æ ç è ö ÷ ø d d yy Vxy , z , () d d æ ç è ö ÷ ø d d + zz Vxy , z , () d d æ ç è ö ÷ ø d d + é ê ë ù ú û := LapC 1 r r r r Vrf , z , ( ) d d × æ ç è ö ÷ ø d d × 1 r 2 ff Vrf , z , ( ) d d æ ç è ö ÷ ø d d é ê ë ù ú û × + zz Vrf , z , ( ) d d æ ç è ö ÷ ø d d + := LapS 1 r 2 r r 2 r Vr q ,f , ( ) d d × æ ç è ö ÷ ø d d × é ê ë ù ú û 1 r 2 sin q () × q sin q () q Vr q ,f , ( ) d d × æ ç è ö ÷ ø d d × + 1 r 2 sin q () 2 × ff Vr q ,f , ( ) d d d d × + := Poisson’s and Laplace Equations Page 5 Poisson’s and Laplace Equations A useful approach to the calculation of electric potentials Relates potential to the charge density. The electric field is related to the charge density by the divergence relationship The electric field is related to the electric potential by a gradient relationship Therefore the potential is related to the charge density by Poisson's equation In a charge-free region of space, this becomes Laplace's equation Potential of a Uniform Sphere of Charge outside inside Poisson’s and Laplace Equations Poisson’s Equation From the point form of Gaus's Law Del_dot_ D r v Definition D D eE and the gradient relationship E DelV - Del_D Del_ eE () Del_dot_ eDelV ( ) - r v Del_DelV r v - e Laplace’s Equation if r v 0 Del_dot_D r v Del_Del Laplacian The divergence of the gradient of a scalar function is called the Laplacian. LapR xx Vxy , z , () d d æ ç è ö ÷ ø d d yy Vxy , z , () d d æ ç è ö ÷ ø d d + zz Vxy , z , () d d æ ç è ö ÷ ø d d + é ê ë ù ú û := LapC 1 r r r r Vrf , z , ( ) d d × æ ç è ö ÷ ø d d × 1 r 2 ff Vrf , z , ( ) d d æ ç è ö ÷ ø d d é ê ë ù ú û × + zz Vrf , z , ( ) d d æ ç è ö ÷ ø d d + := LapS 1 r 2 r r 2 r Vr q ,f , ( ) d d × æ ç è ö ÷ ø d d × é ê ë ù ú û 1 r 2 sin q () × q sin q () q Vr q ,f , ( ) d d × æ ç è ö ÷ ø d d × + 1 r 2 sin q () 2 × ff Vr q ,f , ( ) d d d d × + := Poisson’s and Laplace Equations Given Vxy , z , ( ) 4y × z × x 2 1 + := x y z æ ç ç è ö ÷ ÷ ø 1 2 3 æ ç ç è ö ÷ ÷ ø := eo 8.85410 12 - × := Vxy , z , ( ) 12 = Find: V @ and r v at P LapR xx Vxy , z , ( ) d d æ ç è ö ÷ ø d d yy Vxy , z , ( ) d d æ ç è ö ÷ ø d d + zz Vxy , z , ( ) d d æ ç è ö ÷ ø d d + é ê ë ù ú û := LapR 12 = rv LapR eo × := rv 1.062 10 10 - ´ = Examples of the Solution of Laplace’s Equation D7.1Read More
|
10 videos|45 docs|56 tests
|
FAQs on PPT: Poisson’s & Laplace Equations - Electromagnetic Fields Theory (EMFT) - Electrical Engineering (EE)
| 1. What is Poisson's equation and how is it used in physics? |  |
Ans. Poisson's equation is a partial differential equation that relates the distribution of a scalar field to its sources in physics. It is commonly used to describe phenomena such as the electric potential, gravitational potential, or fluid flow. By solving Poisson's equation, we can determine the potential or field distribution caused by the given sources.
| 2. What is Laplace's equation and why is it important in electrostatics? | |
Ans. Laplace's equation is a second-order partial differential equation that describes the behavior of scalar fields in physics. In electrostatics, Laplace's equation is used to model the electric potential in regions where there are no charges or external sources. Solving Laplace's equation allows us to determine the electric potential in these regions, which is crucial for understanding the behavior of electric fields and charges.
| 3. How are Poisson's and Laplace's equations related? | |
Ans. Poisson's equation is derived from Laplace's equation by introducing a source term. While Laplace's equation describes the behavior of scalar fields in regions without sources, Poisson's equation accounts for the presence of sources. Thus, Poisson's equation can be seen as an extension of Laplace's equation that incorporates the effect of sources on the field distribution.
| 4. Can Poisson's and Laplace's equations be solved analytically? | |
Ans. Yes, Poisson's and Laplace's equations can be solved analytically in certain cases. If the boundary conditions and sources are simple enough, it is possible to find analytical solutions using techniques such as separation of variables or Fourier series. However, in more complex situations, numerical methods like finite difference or finite element methods are often employed to approximate the solutions.
| 5. What are some applications of Poisson's and Laplace's equations in engineering and science? | |
Ans. Poisson's and Laplace's equations have numerous applications in various fields of engineering and science. Some examples include the analysis of electric and magnetic fields, fluid dynamics, heat conduction, and quantum mechanics. These equations are fundamental tools for understanding and solving a wide range of physical problems, making them essential in fields such as electrical engineering, physics, and computational science.
About this Document
|
4.93/5 Rating |
|
Nov 22, 2024 Last updated |
Document Description: PPT: Poisson’s & Laplace Equations for Electrical Engineering (EE) 2024 is part of Electromagnetic Fields Theory (EMFT) preparation.
The notes and questions for PPT: Poisson’s & Laplace Equations have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about PPT: Poisson’s & Laplace Equations covers topics
like and PPT: Poisson’s & Laplace Equations Example, for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for PPT: Poisson’s & Laplace Equations.
Introduction of PPT: Poisson’s & Laplace Equations in English is available as part of our Electromagnetic Fields Theory (EMFT)
for Electrical Engineering (EE) & PPT: Poisson’s & Laplace Equations in Hindi for Electromagnetic Fields Theory (EMFT) course.
Download more important topics related with notes, lectures and mock test series for Electrical Engineering (EE)
Exam by signing up for free. Electrical Engineering (EE): PPT: Poisson’s & Laplace Equations | Electromagnetic Fields Theory (EMFT) - Electrical Engineering (EE)
Description
Full syllabus notes, lecture & questions for PPT: Poisson’s & Laplace Equations | Electromagnetic Fields Theory (EMFT) - Electrical Engineering (EE) - Electrical Engineering (EE) | Plus excerises question with solution to help you revise complete syllabus for Electromagnetic Fields Theory (EMFT) | Best notes, free PDF download
Information about PPT: Poisson’s & Laplace Equations
In this doc you can find the meaning of PPT: Poisson’s & Laplace Equations defined & explained in the simplest way possible. Besides explaining types of
PPT: Poisson’s & Laplace Equations theory, EduRev gives you an ample number of questions to practice PPT: Poisson’s & Laplace Equations tests, examples and also practice Electrical Engineering (EE)
tests
|
10 videos|45 docs|56 tests
|
Download as PDF
|
Explore Courses for Electrical Engineering (EE) exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
mock tests for examination
,study material
,MCQs
,Viva Questions
,Important questions
,Summary
,Previous Year Questions with Solutions
,past year papers
,practice quizzes
,PPT: Poisson’s & Laplace Equations | Electromagnetic Fields Theory (EMFT) - Electrical Engineering (EE)
,Exam
,shortcuts and tricks
,Objective type Questions
,PPT: Poisson’s & Laplace Equations | Electromagnetic Fields Theory (EMFT) - Electrical Engineering (EE)
,Sample Paper
,ppt
,Extra Questions
,PPT: Poisson’s & Laplace Equations | Electromagnetic Fields Theory (EMFT) - Electrical Engineering (EE)
,Semester Notes
,video lectures
,Free
;
Additional Information about PPT: Poisson’s & Laplace Equations for Electrical Engineering (EE) Preparation
PPT: Poisson’s & Laplace Equations Free PDF Download
The PPT: Poisson’s & Laplace Equations is an invaluable resource that delves deep into the core of the Electrical Engineering (EE) exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner,
allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material,
or toppers' notes, this PDF has got you covered. Download the PPT: Poisson’s & Laplace Equations now and kickstart your journey towards success in the Electrical Engineering (EE) exam.
Importance of PPT: Poisson’s & Laplace Equations
The importance of PPT: Poisson’s & Laplace Equations cannot be overstated, especially for Electrical Engineering (EE) aspirants.
This document holds the key to success in the Electrical Engineering (EE) exam.
It offers a detailed understanding of the concept, providing invaluable insights into the topic.
By knowing the concepts well in advance, students can plan their preparation effectively.
Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.
PPT: Poisson’s & Laplace Equations Notes
PPT: Poisson’s & Laplace Equations Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to PPT: Poisson’s & Laplace Equations.
It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation.
Practice papers and question papers enable you to assess your progress effectively.
Additionally, the paper analysis provides valuable tips for tackling the exam strategically.
Access to Toppers' notes gives you an edge in understanding complex concepts.
Whether you're a beginner or aiming for advanced proficiency, PPT: Poisson’s & Laplace Equations Notes on EduRev are your ultimate resource for success.
PPT: Poisson’s & Laplace Equations Electrical Engineering (EE) Questions
The "PPT: Poisson’s & Laplace Equations Electrical Engineering (EE) Questions" guide is a valuable resource for all aspiring students preparing for the
Electrical Engineering (EE) exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study PPT: Poisson’s & Laplace Equations on the App
Students of Electrical Engineering (EE) can study PPT: Poisson’s & Laplace Equations alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the PPT: Poisson’s & Laplace Equations,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of PPT: Poisson’s & Laplace Equations is prepared as per the latest Electrical Engineering (EE) syllabus.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup