Physics Asked on January 4, 2022

So Anderson et al proposed a model to explain the production of Sub Auroral Ion Drifts. In the paper they talk about how the decrease in ionospheric conductance results in an increase in the electric field, but why is this so?

I understand that decrease in conductance is an increase in resistivity. By Ohm’s law $V = IR$ and thus $V$ increases, but since $E = -displaystylefrac{dV}{dx}$ shouldn’t $E$ decrease if conductance decreases ?

In the paper they talk about how the decrease in ionospheric conductance results in an increase in the electric field, but why is this so?

This just results from Ohm's law and some assumptions about the system. The generalized Ohm's law can be written as:
$$
mathbf{E} + mathbf{v} times mathbf{B} approx frac{ mathbf{j} times mathbf{B} }{ n e } - frac{ nabla}{ n e } cdot left( mathcal{P}_{e} + frac{ m_{e} }{ m_{i} } mathcal{P}_{i} right) + eta mathbf{j} + frac{ m_{e} }{ n e^{2} } frac{ d mathbf{j} }{ d t } tag{0}
$$
where $mathbf{j}$ is the total current density, $n$ is the total number density (assuming *quasi-neutrality*, i.e., $n_{e} = n_{i}$), $e$ is the fundamental charge, $mathcal{P}_{s}$ is the pressure tensor of species $s$, $m_{s}$ is the mass of species $s$ ($s$ can be $e$ for electron or $i$ for ion), and $eta$ is the scalar electrical resistivity (see also https://physics.stackexchange.com/a/438272/59023 or https://physics.stackexchange.com/a/363523/59023 or https://physics.stackexchange.com/a/261223/59023 for more on Ohm's law and conductivities). Typically, many of these terms are small enough to be negligible and one can approximate the electric field as:
$$
mathbf{E} approx eta mathbf{j} tag{1}
$$
Note that $eta^{-1} = sigma$ which is the electrical conductivity. So for situations where the current is held constant but $sigma$($eta$) decreases(increases), the magnitude of $mathbf{E}$ must increase accordingly. Situations like this can arise when there's a constant input source for the current from an external driver.

As an aside, one generally does not drop several of the terms I ignored here in generalized Ohm's law for the ionosphere because they are not always negligible in this region. I merely did so to help simplify the point.

Answered by honeste_vivere on January 4, 2022

It's probably this:

To sustain a field requires a potential difference between two points. if the path between those two points is conductive, a small current will flow between them, the potential difference gets bled away, and the strength of the field diminishes. If the conductance between them is low, no current will flow, the charge imbalance will be sustained, and the strength of the field is not diminished.

Answered by niels nielsen on January 4, 2022

1 Asked on December 31, 2020 by julien-pitteloud

causality closed timelike curve curvature determinism general relativity

0 Asked on December 31, 2020 by adarsh-payyavula

1 Asked on December 31, 2020 by littlegiant

casimir effect quantum field theory quantum mechanics vacuum

1 Asked on December 31, 2020 by catomaths

1 Asked on December 31, 2020 by s-low

anticommutator causality commutator fermions quantum field theory

2 Asked on December 31, 2020

1 Asked on December 30, 2020 by p2000

electromagnetic induction electromagnetism magnetic fields maxwell equations

0 Asked on December 30, 2020

1 Asked on December 30, 2020 by jfearn

2 Asked on December 30, 2020 by user1760043

forces newtonian mechanics reference frames rotational dynamics

5 Asked on December 30, 2020 by murshid-badawi

aerodynamics bernoulli equation everyday life fluid dynamics pressure

2 Asked on December 30, 2020 by flyingwaffle

1 Asked on December 30, 2020 by chandrahas

1 Asked on December 30, 2020 by sandesh-kalantre

classical mechanics constrained dynamics degrees of freedom lagrangian formalism spacetime dimensions

2 Asked on December 30, 2020 by dennis-jaheruddin

optics refraction speed of light variational principle visible light

6 Asked on December 30, 2020

0 Asked on December 30, 2020

hilbert space majorana fermions quantum information quantum mechanics trace

2 Asked on December 30, 2020 by tobuslieven

3 Asked on December 30, 2020 by the-homeschooler

angular momentum gyroscopes precession rotational dynamics torque

Get help from others!

Recent Questions

- How Do I Get The Ifruit App Off Of Gta 5 / Grand Theft Auto 5
- Iv’e designed a space elevator using a series of lasers. do you know anybody i could submit the designs too that could manufacture the concept and put it to use
- Need help finding a book. Female OP protagonist, magic
- Why is the WWF pending games (“Your turn”) area replaced w/ a column of “Bonus & Reward”gift boxes?
- Does Google Analytics track 404 page responses as valid page views?

Recent Answers

- Jon Church on Why fry rice before boiling?
- haakon.io on Why fry rice before boiling?
- Peter Machado on Why fry rice before boiling?
- Lex on Does Google Analytics track 404 page responses as valid page views?
- Joshua Engel on Why fry rice before boiling?

© 2023 AnswerBun.com. All rights reserved. Sites we Love: PCI Database, UKBizDB, Menu Kuliner, Sharing RPP