Electric Charges and Fields

O n a microscopic scale, electric charge is quantized. However, there are often situations in which many charges are so close together that they can be thought of as continuously distributed. The use of a continuous charge density to describe a large number of discrete charges is similar to the use of a continuous mass density to describe air, which actually consists of a large number of discrete molecules. In both cases, it is usually easy to find a volume element V that is large enough to contain a multitude of individual charges or molecules and yet is small enough that replacing V with a differential dV and using calculus introduces negligible error. We describe the charge per unit volume by the volume charge density r: 22-1 Often charge is distributed in a very thin layer on the surface of an object. We define the surface charge density s as the charge per unit area:

Electrostatic Force (charges at rest): • Electrostatic force can be attractive • Electrostatic force can be repulsive • Electrostatic force acts through empty space • Electrostatic force much stronger than gravity • Electrostatic forces are inverse square law forces (proportional to 1/r 2) • Electrostatic force is proportional to the product of the amount of charge on each interacting object Magnitude of the Electrostatic Force is given by Coulomb's Law: F = K q 1 q 2 /r 2 (Coulomb's Law) where K depends on the system of units K = 8.99x10 9 Nm 2 /C 2 (in MKS system) K = 1/(4πε πε 0) where ε ε 0 = 8.85x10-12 C 2 /(Nm 2) Electric Charge: electron charge =-e e = 1.6x10-19 C proton charge = e C = Coulomb Electric charge is a conserved quantity (net electric charge is never created or destroyed!) q 1 q 2 r

2013

Utilizing the integral expression of Coulomb's Law to determine the electric potential from a continuous charge distribution is a canonical exercise in Electricity and Magnetism (E&M). In this study, we use both think-aloud interviews and responses to traditional exam questions to investigate student difficulties with this topic at the upper-division level. Leveraging a theoretical framework for the use of mathematics in physics, we discuss how students activate, construct, execute and reflect on the integral form of Coulomb's Law when solving problems with continuous charge distributions. We present evidence that junior-level E&M students have difficulty mapping physical systems onto the mathematical expression for the Coulomb potential. Common challenges include difficulty expressing the difference vector in appropriate coordinates as well as determining expressions for the differential charge element and limits of integration for a specific charge distribution. We discuss possible implications of these findings for future research directions and instructional strategies.

A system is composed of a circular ring of radius uniformly charged with total charge and a straight wire of length with linear charge density = 0 (−). One of the ends of the charged wire coincides with the center of the ring, as shown in the figure 1. Determinate the electric force that the ring exerts on the wire and the electric force that the wire exerts on the ring.

A fundamental question in physics is how do opposite charges attract and similar charges repel. What exactly is ‘charge’ and what exists between these charges that allows the transmission of these forces? This paper explains the electrostatic force as being the result of phased wave interactions between positive and negative charges. These waves are mediated by a special neutrally charged medium which transmits both normal electromagnetic waves and the special high frequency waves which make up the electrostatic force.

Interaction between electric charges is examined from positions of the etheric screens theory as an interaction of the bodies in systems of two bodies with equal and different screening areas. Such systems are characteristic by the existence therein of zones of attraction and zones of repelling. The borders between zones of attraction and zones of repelling are placed in these systems at distances from the center of rotation depending from the values and relation between the screening areas, the border between zones of attraction and repelling in systems with equal screening areas being maximally distanced from and such border in systems with different screening areas being nearer to the center of rotation.

2021

The paper focuses on the part of the Coulomb’s Law that is just a definition and provides one possible mechanism for operationally defining electric charge based on the concept of force(action at a distance). Then a derivation of Coulomb’s law from the definition is presented and the sign of the charges are defined. Finally, the paper concludes with a discussion on the conservation of charge.

Allpanchis, 2024

analyze the practices related to home-making among llama pastoralists in the South-Central Andes, a process which is understood as a continuous negotiation among different kinds of persons, both human and nonhuman. I start by conceptualizing pastoralism as a social interaction network involving herders, their animals, the community (as the owner of the land), and various deities. Then, I analyze how llameros negotiate the placement of the house with each one of these agents, according to a logic that is explicitly manifested in ritual. In order to illustrate this point, I describe the k’illpa or «flowering» of the animals, the main domestic ritual of the annual cycle. I put emphasis on the ritual gestures and the way in which they express and reproduce this social fabric which defines the place of each family in the territory and in the world.

Contratto e impresa, 2024

È noto che la differenza tra modificazione e novazione di un rapporto obbligatorio si appunta in termini di compatibilità e/o incompatibilità del rapporto modificato o novato col precedente rapporto. In merito a tale questione, il presente contributo offre alcuni spunti sulla dilazione, se essa debba sempre considerarsi come modificazione del rapporto obbligatorio e se, come sembra propendere la recente giurisprudenza, esistano anche ipotesi in cui l’effetto dilatorio del termine possa derivare da una novazione.