This document discusses electrostatics and electrostatic devices. It begins with an outline of Topic 4, which includes electric fields due to point charges and continuous charge distributions, electric potential, energy in electrostatic fields, and boundary conditions in electrostatics. It then discusses electrostatic devices such as resistors and capacitors. The document provides the equations of Poisson and Laplace, which describe how electric potential varies in volumes. It gives recommendations for solving Laplace's equation and provides recipes for analyzing resistors and capacitors. The goal is to have students make an explanatory video solving 2 electrostatics problems involving continuous charge distributions, electrostatic devices, and Laplace's equation with boundary conditions.
Ya sabemos que los elementos que aportan la energía a un circuito reciben el nombre de elementos activos, también llamados generadores o fuentes. Una fuente de tensión ideal es la que nos suministra una tensión constante independientemente del valor de la intensidad que suministra. Sin embargo, en la realidad, la fuente de tensión tiene una resistencia interna que se puede considerar asociada en serie con la propia fuente, constituyendo lo que llamamos fuente de tensión real.
Ya sabemos que los elementos que aportan la energía a un circuito reciben el nombre de elementos activos, también llamados generadores o fuentes. Una fuente de tensión ideal es la que nos suministra una tensión constante independientemente del valor de la intensidad que suministra. Sin embargo, en la realidad, la fuente de tensión tiene una resistencia interna que se puede considerar asociada en serie con la propia fuente, constituyendo lo que llamamos fuente de tensión real.
Dielectrics are usually placed between the two plates of parallel plate capacitors. They can fully occupy the region between the plates or can partially occupy. Copy the link given below and paste it in new browser window to get more information on Effect of Dielectric on Capacitance www.askiitians.com/iit-jee-electrostatics/effect-of-dielectric-on-capacitance/
Dielectrics are usually placed between the two plates of parallel plate capacitors. They can fully occupy the region between the plates or can partially occupy. Copy the link given below and paste it in new browser window to get more information on Effect of Dielectric on Capacitance www.askiitians.com/iit-jee-electrostatics/effect-of-dielectric-on-capacitance/
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
2. Esquema del Tema 04
Campo eléctrico debido a cargas puntuales
Campo eléctrico debido a una distribución continua de cargas
Potencial eléctrico
Energía en campos electroestáticos
Condiciones de borde en electroestática
Dispositivos electroestáticos
2
4a
4b
4c
4d
4e
4f
4. Agenda
4
• Ecuación de Poisson.
• Ecuación de Laplace.
• Resistores.
• Capacitores.
• Ejemplo de aplicación de los conceptos.
5. Ecuación de Poisson
Medio Inhomogéneo Medio Homogéneo
• La permitividad es constante en todo el
medio (no varía)
5
V
V
V
V
2 V
V
6. Ecuación de Laplace
Medio Inhomogéneo Medio Homogéneo
• La permitividad es constante en todo el
medio (no varía)
6
0
V
2 V
V
2
0
V
La ecuación de Laplace es un caso particular de Poisson, cuando la carga es nula
Laplaciano
2
7. Ecuación de Laplace
7
¿Bajo qué condiciones no hay carga en electrostática?
+ + + + + + + + + + + + +
− − − − − − − − − − − − −
No hay carga entre las placas
2
0
V
8. Ecuación de Laplace y Ecuación de Poisson
Nombre Medio Inhomogéneo Medio Homogéneo
Ecuación de Poisson
Ecuación de Laplace
8
Notas
V
V
0
V
2 V
V
2
0
V
• Las ecuaciones de Poisson y Laplace describen como un potencial eléctrico varía a lo largo de un
volumen.
• Son ecuaciones diferenciales escalares, usualmente más fácil de resolver que ecuaciones
diferenciales vectoriales.
• Usar Poisson cuando hay carga y Laplace cuando ésta no existe.
• La ecuación de Laplace es importante en electrostática porque puede ser usada para calcular el
potencial eléctrico alrededor de conductores mantenidos a diferentes voltajes.
• El teorema de la singularidad indica que no existe solución única.
9. Ecuación de Laplace y Ecuación de Poisson
9
Recomendaciones para resolver ecuación de Laplace
Las ecuaciones de Laplace se resuelve como un problema de frontera (i.e., ecuaciones diferenciales
parciales más condiciones de borde)
1. Seleccionar el sistema de coordenadas a conveniencia que simplifique las matemáticas.
2. Resolver la ecuación de Laplace ∇2𝑉 = 0 en cada región homogénea
1. Cuando el V está en función de sólo una variable, usar integración directa.
2. Caso contrario, usar separación de variables (superposición).
3. Aplicar las condiciones de frontera a los bordes de la región homogénea.
4. Calcular 𝐸 a partir de 𝑉 usando 𝐸 = −∇𝑉.
5. Calcular 𝐷 a partir de 𝐸 usando 𝐷 = 𝜀𝐸.
10. Resistores
• Un resistor es un elemento pasivo, de dos terminales, que limita
la conductividad del sistema, por tanto limitando el fujo de
corriente.
10
12. Resistores
12
S
V
R
I
I
V
J
• Ley de Ohm
• Intensidad de Campo Eléctrico
• Densidad de Corriente Eléctrica
J E
V
E
En un Medio Homogéneo
R
S S
I
J
S
13. Resistores
13
S
V
R
I
I
V
J
Considerando un análisis electromagnético
• Voltaje en el conductor
• Corriente a través del conductor
V E d
En un Medio no-Homogéneo
S
E d
R
E ds
S
I J ds
S
E ds
14. Resistores
14
Receta para analizar un resistor
1. Seleccionar el sistema de coordenadas a conveniencia que simplifique las matemáticas.
2. Asumir 𝑉0 como el potencial de referencia a través de los terminales del conductor.
3. Calcular el potencial eléctrico 𝑉 resolviendo la ecuación de Laplace ∇2𝑉 = 0.
4. Calcular 𝐸 usando 𝐸 = −∇𝑉.
5. Calcular 𝐼 a partir de 𝐼 = 𝑆
𝜎𝐸 ⋅ 𝑑𝑠.
6. Calcular 𝑅 usando 𝑅 = 𝑉0
𝐼.
15. Capacitores
• Un capacitor es un componente eléctrico pasivo de dos
terminales, el cual permite almacenar y liberar energía eléctrica.
Proporciona una corriente tal que el voltaje entre sus terminales
se mantiene constante.
15
16. Capacitores
• Se define como capacitancia a la magnitud de la carga en una de las placas a la
diferencia de potencial entre las dos placas.
16
Concepto de Capacitancia
Q
Q
0
Q
C
V
17. Capacitores
17
Receta para analizar un capacitor
1. Seleccionar el sistema de coordenadas a conveniencia que simplifique las matemáticas.
2. Identificar que placas acarrea que carga, +𝑄 y −𝑄.
3. Calcular 𝐷 usando la Ley de Gauss.
4. Calcular 𝐸 usando 𝐸 = 𝐷
𝜀.
5. Calcular 𝑉0 usando 𝑉0 = − 𝐿
𝐸 ⋅ 𝑑ℓ.
6. Calcular 𝐶 usando 𝐶 = 𝑄
𝑉0
.
20. Actividades Asíncronas, S06
Actividad Grupal: Hacer video explicativo (max. 20 min.) sobre:
• Plantear y desarrollar 2 problemas sobre electroestática, que incluyan:
• Tema 04: Electrostática
• Campo eléctrico debido a una distribución continua de cargas.
• Dispositivos electroestáticos.
• Ecuación de Laplace (condición de borde).
• REF: SADIKU cap.4, cap.5
• Entregable: video en plataforma MS Stream.
• Responder Quiz (sumativo) : Tema 4