Electromagnetic Fields Wangsness
Yi Pressimone
The Wangsness condition is a boundary condition that applies to electromagnetic fields at an interface between two media. It states that the tangential component of the electric field must be continuous across the boundary, while the tangential component of the magnetic field can have a discontinuity.
The Wangsness condition is important in solving for the behavior of electromagnetic fields at interfaces, such as between different materials or in the presence of conducting surfaces. It ensures that the fields behave in a physically realistic manner and allows for accurate predictions of the behavior of EM waves.
Yes, the Wangsness condition can be violated in certain situations. For example, at the interface between two materials with significantly different permeabilities, the magnetic field may have a discontinuity. In these cases, special techniques such as matching layers can be used to ensure a smooth transition between the two media.
No, the Wangsness condition applies to all types of electromagnetic fields, including static fields, time-varying fields, and waves. It is a fundamental principle in the study of electromagnetism and is essential for understanding the behavior of EM fields in various situations.
The Wangsness condition is named after its discoverer, physicist Dean B. Wangsness, who first published his findings in 1953. Wangsness was studying the behavior of electromagnetic fields at interfaces and found that the tangential component of the electric field must be continuous, leading to the development of this important boundary condition.
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This study reports on the theory of operation, design principles, and results from laboratory and field tests of a magnetic telemetry system for communication with underground infrastructure sensors using rotating permanent magnets as the sources and compact magnetometers as the receivers. Many cities seek ways to monitor underground water pipes with centrally managed Internet of Things (IoT) systems. This requires the development of numerous reliable low-cost wireless sensors, such as moisture sensors and flow meters, which can transmit information from subterranean pipes to surface-mounted receivers. Traditional megahertz radio communication systems are often unable to penetrate through multiple feet of earthen and manmade materials and have impractically large energy requirements which preclude the use of long-life batteries, require complex (and expensive) built-in energy harvesting systems, or long leads that run antennas near to the surface. Low-power magnetic signaling systems do not suffer from this drawback: low-frequency electromagnetic waves readily penetrate through several feet of earth and water. Traditional magnetic telemetry systems that use energy-inefficient large induction coils and antennas as sources and receivers are not practical for underground IoT-type sensing applications. However, rotating a permanent magnet creates a completely reversing oscillating magnetic field. The recent proliferation of strong rare-earth permanent magnets and high-sensitivity magnetometers enables alternative magnetic telemetry system concepts with significantly more compact formats and lower energy consumption. The system used in this study represents a novel combination of megahertz radio and magnetic signaling techniques for the purposes of underground infrastructure monitoring. In this study, two subterranean infrastructure sensors exploit this phenomenon to transmit information to an aboveground radio-networked magnetometer receiver. A flow meter uses a propeller to directly rotate a diametrically magnetized neodymium magnet. A moisture sensor rotates a magnet with a low-power electric motor. Laboratory performance and field tests establish the capabilities of magnetic telemetry for IoT-linked leak-detection sensors. Remote datalogging with encryption demonstrates the viability of integrating sensors and surface receivers into a LoRa wireless IoT network.
Leak detection has three primary goals: quantifying amount of water loss, identification of leak location, and the development of leakage control models (Puust et al., 2010). These goals are achieved in several ways: on-site pipe inspection, statistical modeling of past known failures, modeling of physical pipe/soil attributes, and evaluation of the impacts of specific pipe failure modes (Liu and Kleiner, 2013). Non-intrusive non-destructive testing is especially important so as to avoid water shutoffs which are disruptive to customers, and can cause disturbance of internal pipe tuberculation (Rajani and Kleiner, 2004). Methods of on-site pipe inspection include acoustic detection (Khulief et al., 2012), laser-scanning of pipe interiors, magnetic flux leakage measurements, remote field eddy current detection, broadband electromagnetic sensing, pulsed eddy current testing, (Liu and Kleiner, 2013), and ground penetrating radar (Huston et al., 2017). Not all inspection techniques work for all pipe materials and diameters (Rajani and Kleiner, 2004), however, which complicates the inspection process. Furthermore, detection sensitivity challenges are omnipresent. For example, water leaks at pipe joints and fittings often have flow rates too low to be identified with acoustic detection methods (Lambert, 2002).
A strategy to improve underground utility operations is to use multiple sensors and the IoT to determine the state of infrastructure, including flow levels, leak detection, and unauthorized usage. An example of underground infrastructure sensor networking is in the city of South Bend, Indiana, USA, with CSOnet, which provides real-time control of storm water infrastructure for combined sewer overflow abatement (Montestruque and Ruggaber, 2007). A challenge is that communication with sensors in and around subterranean water utilities is often obstructed by asphalt, rebar, concrete, manhole covers, in addition to several feet of earth and soil. Low-power megahertz radio systems, such as LoRa, do not transmit well through these obstacles (Montestruque and Lemmon, 2008). As the 900 MHz radio used in the CSOnet system was unable to broadcast out of the South Bend sewer system, wireless networking required replacing iron and steel manhole covers with customized fiberglass alternatives, which contained embedded radio antennas (Montestruque and Lemmon, 2008).
The penetrating ability of magnetic signaling makes it well-suited for direct communication with sensors used for monitoring underground utilities, without the need for modifications to existing infrastructure such as manhole covers. Most materials, including earth and sea water, do not interact with magnetic fields that oscillate below 3,000 Hz, making magnetic signaling compatible with the demands of low-bitrate through-earth communication with buried infrastructure.
Large electric induction coils, or massive antennas that resonate with the desired transmission frequency, are the traditional method of generating and receiving low-frequency magnetic fields. The physical principle is the linear motion of charged particles, i.e., electrons, through conductors creates and receives magnetic fields. The wavelengths of low frequency electromagnetic waves range from tens to thousands of kilometers, making these traditional antenna designs impracticably large and expensive for most applications (Huston, 2017). Only in the past several years have low-cost alternatives become viable (Picos et al., 2016). The recent proliferation of inexpensive, high sensitivity magnetometers has dramatically increased the range of possible applications for magnetic signaling and sensing. The movement of permanent magnets is an alternative means of generating magnetic fields (Gerginov, 2017). The physical principle is that the spin and orbital angular momentum of electrons produces magnetic dipole fields bound in location and orientation to the solid magnet (Moon, 1984). Oscillating movements of the magnets produce oscillating magnetic fields. Powerful rare-earth magnets show promise for the development of smaller, lighter, and stronger signaling sources.
This study uses a simple compact magnetic source based on a rotating permanent magnet, which works well at frequencies up to about 100 Hz. The magnet is a diametrically magnetized neodymium cylinder with a dipole field polarized north-south across its diameter. Rotation about the cylindrical axis causes open field lines to sweep out with the rotation of the cylinder. This creates an alternating oscillating field, as shown in Figure 1.
This study applies a novel combination of these two communication regimes (LoRa megahertz radio, and low-frequency magnetic signaling) for the development of an inexpensive, low-power IoT system, which is able to pass information from subterranean sensors to an aboveground IoT network. These sensors are designed for the purpose of leak detection in a municipal water system. One strategy for leak detection is to use flow meters to monitor for flow rate or volume changes (Zhang, 1996). In this scheme, a rapid change in flow rate at a pipe inlet or outlet may indicate that a leak has developed. Similarly, a leak can also be indicated if the difference between an upstream and a downstream flow measurement exceeds a predefined tolerance (Zhang, 1996). Another leak detection strategy is to use moisture sensors to monitor the moisture content of soil around buried pipes (Christodoulou et al., 2010). A localized area of high moisture may indicate a pipe leak in that location. In this paper, two sensors are developed which take advantage of these leak detection techniques: a self-powered flow meter with magnetic signaling, and a battery powered moisture sensor with magnetic signaling.
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