scholarly journals A Look into Students' Interpretation of Electric Field Lines

2017 ◽  
pp. 342-364
Author(s):  
Esmeralda Campos ◽  
Genaro Zavala
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Random Sample ◽  
Qualitative Approach ◽  
Undergraduate Level ◽  
Field Lines

On Electricity & Magnetism (EM) courses at undergraduate level, the concept of electric field poses one of the most relevant and basic topics, along with the concept of magnetic field. Professors and students may use different diagrams as a tool to visualize the electric field, such as vectors or electric field lines. The present study aims to identify how students interpret and use electric field lines as a tool or resource to describe the electric field. Two versions of a test with open-ended questions were administered in Spanish in a private Mexican university to a random sample of students taking the EM course, and were analyzed with a qualitative approach. It was found that students do not interpret electric field lines diagrams correctly, which may lead to misconceptions. Many students based their answers on the concepts of superposition, force and repulsion.

scholarly journals Mapping of steady-state electric fields and convective drifts in geomagnetic fields – Part 1: Elementary models

2016 ◽  
Vol 34 (1) ◽  
pp. 55-65 ◽  
Author(s):  
A. D. M. Walker ◽  
G. J. Sofko
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Electric Field ◽  
Electric Fields ◽  
Magnetic Field Line ◽  
Geomagnetic Field ◽  
Geomagnetic Field Models ◽  
Spatial Derivatives ◽  
Field Lines ◽  
The Magnetic Field

Abstract. When studying magnetospheric convection, it is often necessary to map the steady-state electric field, measured at some point on a magnetic field line, to a magnetically conjugate point in the other hemisphere, or the equatorial plane, or at the position of a satellite. Such mapping is relatively easy in a dipole field although the appropriate formulae are not easily accessible. They are derived and reviewed here with some examples. It is not possible to derive such formulae in more realistic geomagnetic field models. A new method is described in this paper for accurate mapping of electric fields along field lines, which can be used for any field model in which the magnetic field and its spatial derivatives can be computed. From the spatial derivatives of the magnetic field three first order differential equations are derived for the components of the normalized element of separation of two closely spaced field lines. These can be integrated along with the magnetic field tracing equations and Faraday's law used to obtain the electric field as a function of distance measured along the magnetic field line. The method is tested in a simple model consisting of a dipole field plus a magnetotail model. The method is shown to be accurate, convenient, and suitable for use with more realistic geomagnetic field models.

scholarly journals Very High-Energy Emission from the Direct Vicinity of Rapidly Rotating Black Holes

Galaxies ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 122 ◽  
Author(s):  
Kouichi Hirotani
Keyword(s):  
Magnetic Field ◽  
Black Holes ◽  
Black Hole ◽  
Electric Field ◽  
Gamma Rays ◽  
Accretion Rate ◽  
High Energy ◽  
Relativistic Electrons ◽  
Field Lines ◽  
The Magnetic Field

When a black hole accretes plasmas at very low accretion rate, an advection-dominated accretion flow (ADAF) is formed. In an ADAF, relativistic electrons emit soft gamma-rays via Bremsstrahlung. Some MeV photons collide with each other to materialize as electron-positron pairs in the magnetosphere. Such pairs efficiently screen the electric field along the magnetic field lines, when the accretion rate is typically greater than 0.03–0.3% of the Eddington rate. However, when the accretion rate becomes smaller than this value, the number density of the created pairs becomes less than the rotationally induced Goldreich–Julian density. In such a charge-starved magnetosphere, an electric field arises along the magnetic field lines to accelerate charged leptons into ultra-relativistic energies, leading to an efficient TeV emission via an inverse-Compton (IC) process, spending a portion of the extracted hole’s rotational energy. In this review, we summarize the stationary lepton accelerator models in black hole magnetospheres. We apply the model to super-massive black holes and demonstrate that nearby low-luminosity active galactic nuclei are capable of emitting detectable gamma-rays between 0.1 and 30 TeV with the Cherenkov Telescope Array.

scholarly journals Storm-time ring current: model-dependent results

2012 ◽  
Vol 30 (1) ◽  
pp. 177-202 ◽  
Author(s):  
N. Yu. Ganushkina ◽  
M. W. Liemohn ◽  
T. I. Pulkkinen
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Boundary Conditions ◽  
Electric Fields ◽  
Ring Current ◽  
Current Model ◽  
Current Data ◽  
Storm Events ◽  
Boundary Location ◽  
Field Lines

Abstract. The main point of the paper is to investigate how much the modeled ring current depends on the representations of magnetic and electric fields and boundary conditions used in simulations. Two storm events, one moderate (SymH minimum of −120 nT) on 6–7 November 1997 and one intense (SymH minimum of −230 nT) on 21–22 October 1999, are modeled. A rather simple ring current model is employed, namely, the Inner Magnetosphere Particle Transport and Acceleration model (IMPTAM), in order to make the results most evident. Four different magnetic field and two electric field representations and four boundary conditions are used. We find that different combinations of the magnetic and electric field configurations and boundary conditions result in very different modeled ring current, and, therefore, the physical conclusions based on simulation results can differ significantly. A time-dependent boundary outside of 6.6 RE gives a possibility to take into account the particles in the transition region (between dipole and stretched field lines) forming partial ring current and near-Earth tail current in that region. Calculating the model SymH* by Biot-Savart's law instead of the widely used Dessler-Parker-Sckopke (DPS) relation gives larger and more realistic values, since the currents are calculated in the regions with nondipolar magnetic field. Therefore, the boundary location and the method of SymH* calculation are of key importance for ring current data-model comparisons to be correctly interpreted.

scholarly journals Investigation on High Velocity Plasmas and Field Aligned Currents at High Latitudes

2020 ◽  
pp. 22-29
Author(s):  
J. C. K. Akhila ◽  
C. P. Anil Kumar
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
High Velocity ◽  
Transmission Function ◽  
External Loading ◽  
Plasma Parameters ◽  
Spherical Cap ◽  
Field Aligned Current ◽  
Field Lines ◽  
Spherical Cap Harmonic Analysis

The interaction of high velocity plasma with Earth’s magnetic field is fundamental and offer many questions on high latitude electrodynamics. The problems associated with influence of electric field and Field Aligned Current (FAC) generation is investigated with the aid of spherical cap harmonic analysis at 830 Mag. Lat. in southern hemispheres. The investigation is done on the cases with different Interplanetary Magnetic Field (IMF) conditions after the earth directed solar events. The helio-plasma parameters viz., density, velocity, energy, electron temperature are also noted during the field aligned current studies. It seems that, due to external magnetic field influence polarization of plasma electric field take place (reorientation of the convective cells). It happens with different orientation as per the magnitude and direction of By and Bz component and the horizontal currents. It is noted that the FAC value also depends on kinetic energy of the plasma streams and conductivity of external loading. As the plasma decelerates by force Jsw X Esw, the resultant current may extend along the field lines. Increases in the FAC density are seemed to be proportional to the transmission function.

scholarly journals Global MHD Simulation of the Weak Southward IMF Condition for Different Time Resolutions

2021 ◽  
Vol 8 ◽  
Author(s):  
Kyung Sun Park
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Magnetic Reconnection ◽  
Three Dimensional ◽  
Slow Solar Wind ◽  
Polar Cap ◽  
Plasma Properties ◽  
Simulation Results ◽  
Field Lines ◽  
The Impact

We performed high-resolution three-dimensional global MHD simulations to determine the impact of weak southward interplanetary magnetic field (IMF) (Bz = −2 nT) and slow solar wind to the Earth’s magnetosphere and ionosphere. We considered two cases of differing, uniform time resolution with the same grid spacing simulation to find any possible differences in the simulation results. The simulation results show that dayside magnetic reconnection and tail reconnection continuously occur even during the weak and steady southward IMF conditions. A plasmoid is generated on closed plasma sheet field lines. Vortices are formed in the inner side of the magnetopause due to the viscous-like interaction, which is strengthened by dayside magnetic reconnection. We estimated the dayside magnetic reconnection which occurred in relation to the electric field at the magnetopause and confirmed that the enhanced electric field is caused by the reconnection and the twisted structure of the electric field is due to the vortex. The simulation results of the magnetic field and the plasma properties show quasi-periodic variations with a period of 9–11 min between the appearances of vortices. Also the peak values of the cross-polar cap potential are both approximately 50 kV, the occurrence time of dayside reconnections are the same, and the polar cap potential patterns are the same in both cases. Thus, there are no significant differences in outcome between the two cases.

scholarly journals Centrifugal acceleration of protons by a supermassive black hole

2020 ◽  
Vol 492 (4) ◽  
pp. 4884-4891 ◽  
Author(s):  
Ya N Istomin ◽  
A A Gunya
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Galactic Nuclei ◽  
Rotation Frequency ◽  
Azimuthal Velocity ◽  
Lorentz Factor ◽  
Centrifugal Acceleration ◽  
Poloidal Magnetic Field ◽  
Field Lines ◽  
Sgr A

ABSTRACT Centrifugal acceleration is due to the rotating poloidal magnetic field in the magnetosphere that creates the electric field which is orthogonal to the magnetic field. Charged particles with finite cyclotron radii can move along the electric field and receive energy. Centrifugal acceleration pushes particles to the periphery, where their azimuthal velocity reaches the speed of light. We calculated particle trajectories by numerical and analytical methods. The maximum obtained energies depend on the parameter of the particle magnetization κ, which is the ratio of rotation frequency of magnetic field lines in the magnetosphere ΩF to non-relativistic cyclotron frequency of particles ωc, κ = ΩF/ωc <<1, and on the parameter α which is the ratio of toroidal magnetic field BT to the poloidal one BP, α = BT/BP. It is shown that for small toroidal fields, α < κ1/4, the maximum Lorentz factor γm is only the square root of magnetization, γm = κ−1/2, while for large toroidal fields, α > κ1/4, the energy increases significantly, γm = κ−2/3. However, the maximum possible acceleration, γm = κ−1, is not achieved in the magnetosphere. For a number of active galactic nuclei, such as M87, maximum values of Lorentz factor for accelerated protons are found. Also, for special case of Sgr. A*, estimations of the maximum proton energy and its energy flux are obtained. They are in agreement with experimental data obtained by HESS Cherenkov telescope.

Trade-off in perpendicular electric field control using negatively biased emissive end-electrodes

2022 ◽  
Author(s):  
Baptiste Trotabas ◽  
Renaud Gueroult
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Thermionic Emission ◽  
Potential Drop ◽  
Plasma Potential ◽  
Magnetized Plasma ◽  
Trade Off ◽  
Sheath Edge ◽  
Field Control ◽  
Field Lines

Abstract The benefits of thermionic emission from negatively biased electrodes for perpendicular electric field control in a magnetized plasma are examined through its combined effects on the sheath and on the plasma potential variation along magnetic field lines. By increasing the radial current flowing through the plasma thermionic emission is confirmed to improve control over the plasma potential at the sheath edge compared to the case of a cold electrode. Conversely, thermionic emission is shown to be responsible for an increase of the plasma potential drop along magnetic field lines in the quasi-neutral plasma. These results suggest that there exists a trade-off between electric field longitudinal uniformity and amplitude when using negatively biased emissive electrodes to control the perpendicular electric field in a magnetized plasma.

scholarly journals Mapping of steady-state electric fields and convective drifts in geomagnetic fields – Part 2: The IGRF

2016 ◽  
Vol 34 (1) ◽  
pp. 67-73 ◽  
Author(s):  
A. D. M. Walker
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Field Line ◽  
Electric Fields ◽  
Rate Of Change ◽  
International Geomagnetic Reference Field ◽  
First Order ◽  
Faraday’S Law ◽  
Geomagnetic Fields ◽  
Field Lines

Abstract. A method of mapping electric fields along geomagnetic field lines is applied to the IGRF (International Geomagnetic Reference Field) model. The method involves integrating additional sets of first order differential equations simultaneously with those for tracing a magnetic field line. These provide a measure of the rate of change of the separation of two magnetic field lines separated by an infinitesimal amount. From the results of the integration Faraday's law is used to compute the electric field as a function of position along the field line. Examples of computations from a software package developed to implement the method are presented. This is expected to be of use in conjugate studies of magnetospheric phenomena such as SuperDARN (Super Dual Auroral Radar) observations of convection in conjugate hemispheres, or comparison of satellite electric field observations with fields measured in the ionosphere.

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