Let the 4 vertices of a particular tetrahedron (blue profile) exist as half the vertices of a unit cube.
Let the base vertices be one unit away from the fourth (apex) vertex as shown in the diagram above.
Given only this information find the height (H) and volume (V) of the tetrahedron.
Hint: The formula for the volume of a tetrahedron is one third the area of the base times the height H.
The energy carried by an electromagnetic (E-M) wave with field intensities E, B is given by the Poynting vector, S:
S = 1/mo [E X B]
The preceding is the most elementary form usually presented in the 2nd semester of Calculus physics. But in this post I want to treat the more advanced (graduate) level form:
S = 1/mo [E X B] =
mo / c {[ Po w2 / 4p ] sin q/ r cos w2 (t - r/c)]}2 r^
From here we proceed by taking the time average, i.e.:
<S> = (mo / c )Po 2 w4 / 32 p 2 sin 2 q/ r2 r^
Then the total power radiated:
Ptotal = mo Po 2 w4 / 32 p 2 c ò 2p o df ò p o sin 2 q sin q dq
And:
ò p o sin 2 q sin q dq = ò p o sin 3 q dq = - cos q + cos3 q / 3 ] p o
= - 1 - 1/3 - (-1 + 1/3) = 6/3 - 2/3 = 4/3
And:
ò 2p o df = 2 p
Þ
Ptotal =
mo Po 2 w4 / 32 p 2 c (2 p) (4/3) = 8p /3 [ mo Po 2 w4 / 32 p 2 c]
Ptotal = mo Po 2 w4 / 12 p c
This amounts to the energy radiated from a Hertzian dipole, which is the largest of all types of dipole configuration.
Suggested Problem:
Find the total average power (Ptotal av = Prad ) radiated by a Hertzian dipole over a closed sphere of radius r. (Take ho as the impedance of free space, with Io the steady current and k = w /c the wave number.)
The real Covid scandal was the way in which Trump handled the crisis, which was a disaster and increased the number of deaths significantly. The origins are interesting, but once Covid started to spread, the top priority should have been to contain it, not pass blame. Now, 6 years later, the Republicans are trying to pass blame again while concurrently destroying our public health infrastructure.- WaPo comment
They asked if Fauci was wearing a tie and whether there was a folder on the table, the answers to both being plainly visible, then they removed his attorney, likely violating a right to counsel. That left absolutely no doubt that their goal was to entrap Fauci. Answering any question after invoking The 5th revokes the invoke and opens the witness to abusive charges of contempt. Hawley, Rand, and the others are performative mules, nothing more. .- WaPo comment
Hahaha ...[Trump] 𝘪𝘯𝘷𝘰𝘬𝘦𝘥
𝘩𝘪𝘴
𝘍𝘪𝘧𝘵𝘩
𝘈𝘮𝘦𝘯𝘥𝘮𝘦𝘯𝘵
𝘳𝘪𝘨𝘩𝘵
𝘢𝘨𝘢𝘪𝘯𝘴𝘵
𝘴𝘦𝘭𝘧-𝘪𝘯𝘤𝘳𝘪𝘮𝘪𝘯𝘢𝘵𝘪𝘰𝘯
𝘮𝘰𝘳𝘦
𝘵𝘩𝘢𝘯
440 𝘵𝘪𝘮𝘦𝘴
𝘥𝘶𝘳𝘪𝘯𝘨
𝘢
𝘤𝘭𝘰𝘴𝘦𝘥-𝘥𝘰𝘰𝘳
𝘤𝘪𝘷𝘪𝘭
𝘥𝘦𝘱𝘰𝘴𝘪𝘵𝘪𝘰𝘯
𝘤𝘰𝘯𝘥𝘶𝘤𝘵𝘦𝘥
𝘣𝘺
𝘵𝘩𝘦
𝘕𝘦𝘸
𝘠𝘰𝘳𝘬
𝘈𝘵𝘵𝘰𝘳𝘯𝘦𝘺
𝘎𝘦𝘯𝘦𝘳𝘢𝘭
𝘓𝘦𝘵𝘪𝘵𝘪𝘢
𝘑𝘢𝘮𝘦𝘴'
𝘰𝘧𝘧𝘪𝘤𝘦
𝘰𝘯
𝘈𝘶𝘨𝘶𝘴𝘵
10, 2022
No doubt Trump invoked the 5th Amendment many more times
that we don't know about. If anyone should be "held in contempt" it's
Trump. Oh wait he already is held in contempt by most of the world, and most
Americans. .- WaPo comment
In the U.S. mainstream Media now an idiot is ‘born’ every minute. In this case Peggy Noonan – in her latest WSJ column (Anthony Fauci Unmasks Himself)- where she blurts:
“It wasn’t good for Anthony Fauci or anybody else that he took the Fifth at his Senate hearing this week. That plus his diary may well have been a reputation-destroying event."
Uh, only in your fetid imagination, Pegs, especially given that hearing - dominated by Repuke assholes like Rand Paul (gunning for Fauci since the Covid outbreak)- was just a McCarthy-style gutter show and sham.
While we're at it let's recall Miss Peggy was the dumbo who six years ago actually trotted out this twaddle:
She resorted to this pathetic ploy to try to make the specious case that - like Sonny's family loyalty, i.e. to the Don (Vito Corleone)- Trump is also about family loyalty which trumps (no pun intended) any military service, or higher respect for the military.
Don't buy it? Then check the relevant segment below for
yourselves:
And we're supposed to take her potshots at Anthony Fauci seriously now? Because he justifiably took the Fifth? Give me a freaking break.
But sometimes, maybe not often in this country of media chaos, one steady voice using facts and reason can stem the torrent of lies and political attacks. So kudos to Dr. Celine Gounder for appearing yesterday on CBS Mornings to defend Dr. Anthony Fauci amid rabid Reep Senate attacks led by the Fauci-obsessed Rand Paul.
What brought the Fauci-obsessed Paul to the apoplectic state he displayed yesterday? Well, evidently - according to him - "scrutinizing the release" of
Dr. Fauci’s private diary - then claiming
falsely Fauci been trying to hide the “fact” of secret NIH funding to the Wuhan
lab in China. This was for “gain of purpose” vaccine research – which he claimed led to
the Covid virus escape from that lab.
All of which is recycled horse shit.
As Dr. Gounder patiently explained to the CBS hosts yesterday morning, the gain of purpose vaccine strategy is well known to try to anticipate the next mutations of a virus, say like influenza. That is done to be able to have ready a more effective vaccine should a hitherto unknown form emerge.
As for Dr. Fauci’s diary she informed the hosts she’s read the whole of it (500 pages, not 1,000) and noted the total NIH funding for the Chinese lab over 6 years came to barely $600,000 – or $100, 000 a year. A minimal amount. She also pointed out, again in a calm and steady voice, that the bulk of Dr.Fauci's notes concerned his background efforts to deal with the virus (such as masking) but also the volume of threats to himself and his family.
Why didn't the only remaining living, breathing Senator from Kentucky mention that - or ask about it? Or even condemn the threats on Dr. Fauci's life? Well, because those moves would diminish his grandstanding act to appease the traitor occupying the White House.
To her credit, Dr. Gounder further argued that ongoing political attacks have left U.S. public health "devastated" and criticized the Reep-dominated hearings as partisan witch-hunts rather than constructive reviews. Gounder—an infectious disease specialist, epidemiologist, and CBS News medical contributor—spoke out alongside a letter signed by over 150 medical professionals supporting Dr. Fauci against ongoing harassment. Gounder further made clear that unlike the bipartisan 9/11 Commission which sought genuine lessons and actual information, these congressional probes (led by Reeps) aimed to vilify scientists.
As evidence of the effects of the vilification and ongoing misinformation campaign (mainly by the Trump cabal) she pointed to the multifold damage done by defunding vaccines and sowing even more misinformation, including efforts trying to tie the MMR vaccine) - vaccine to autism. As per a WSJ piece yesterday ('Trump Turns Up Heat On RFK Jr. To Cut Back On Childhood Vaccines, p. A1):
"Trump asked Health and Human Services Secretary Robert F. Kennedy Jr. why he wasn't doing more to probe the alleged connection between vaccines and autism. Kennedy was take aback.....
Chief among the president's desires: Do more to reduce the number of shots that federal guidelines recommend for children."
In other words, the demented lying turd wants the current Measles outbreak to spread even further and with more dire medical consequences like brain swelling, blindness. Why else push to reduce the federal guidelines for the number of shots? But recall, this is the same fungal felon who 6 years ago advocated injecting bleach to remove the virus:
https://www.youtube.com/watch?v=M9kWsUwTcj8
This sort of crap and deliberate assaults on science and Dr. Fauci - with the attendant misinformation - is one reason, as Gounder noted, for the current spread of Measles. As well as failures across the board to monitor foodborne diseases – such as with the current cyclospora outbreak. (After decimating the FDA office charged with monitoring spread of such illnesses as E. coli, salmonella, campylobacter etc.)
Basically, the tired shtick of the Reeptards was to press Fauci for three hours on on whether he was sufficiently truthful in past testimony about the coronavirus pandemic. He made it clear then, over hundreds of hours, his mandate was purely to inform the basis for recommendations for optimal public policy. It was up to state and local officials to carry it out if they felt the information was justified. Many, including former NY governor Cuomo did, as well as former NYC Mayor De Blasio.
But from years past, Dr. Fauci knew the Reeptards like Rand Paul were trying to set a perjury trap for him and then use whatever response he gave against him. In any case, as Dr. Celine Gounder noted, Dr. Fauci had answered hours of questions 6 years earlier when the Reeps questioned him about his Covid 19 safety recommendations. (Dr. Gounder also noting in her interview it was STATE and Local officials who enacted them, not Dr. Fauci.)
Paul, a longtime adversary of Fauci, concluded the nearly three-hour hearing by saying the committee is planning a vote next week on whether to hold Fauci in contempt of Congress. Of course this is pathetic, performative yammering horse manure.
You cannot file a contempt of congress against a citizen who is invoking his
constitutional right! You may be frustrated, you may not like it, but you are obliged to suck it up. As Fauci
proclaimed to the assembled rabid Reepo rats driving the bogus hearing::
“Under the advice of my attorneys, I will invoke my right
under the Fifth Amendment of the Constitution to refrain from answering your
questions,”
Rancid Rand acknowledged to GOP colleagues that there were legal questions about whether Fauci could be held in contempt — citing President Joe Biden’s preemptive pardon of Fauci last year. But the imp contended that Fauci should have just answered questions on Wednesday, even if it meant admitting to a past lie or other wrongdoing.
No, fucktard, he should not have answered any of your already answered (from 6 years earlier) questions. Especially given he knew you were trying to lay a trap for his prosecution. This is given you quislings, traitors, cowards and Trump pecker suckers have no spines to stand on your own.
Hell's bells, why aren't you going after Donnie Dotard for trying to poison people by suggesting the injection of 'disinfectants' in 2020? Huh? Well, because a gaggle of cowards and quislings can't hold their senile master to account.
Fauci’s lawyer, David Schertler, correctly noted that Paul was
fixated on Fauci after their clashes at the height of the pandemic — referring
to a 2021 incident in
which the two men traded accusations of lying — and that the senator’s sole
purpose for the hearing was to punish Fauci and see him in prison.
“The accusations that Chairman Paul continues to propagate are
false and disgraceful, and we will examine all options to hold him
accountable,”
True to their misinformation Zeitgeist, Trump and his criminal White House have embraced the already torpedoed lab leak bunkum, creating a website that calls a lab leak the “true” origin of the pandemic, without sharing any definitive proof.
The true fact is there isn't a scintilla of believable evidence for it. See e.g.
Was coronavirus bioengineered in a lab? Tulane scientist debunks this conspiracy theory
It’s abundantly clear to even the most profound ignoramus that the Reeptards are desperate to relitigate many of the oldest (and already settled) controversies about the Covid response: the safety of mRNA vaccines, the lab leak theory, the lockdowns. Oh, and Dr. Fauci’s alleged role in them, which as I noted was to inform public policy NOT carry it out.
They’d be better served
asking why Trump deliberately suggested poisoning millions with his bleach
injection. Or do they treat that as ‘Trump just being Trump’? Or just a joke?
But no, they lack the balls as well as spines. Especially Josh Hawley who got off on asking Dr. Fauci what color tie he was wearing to try to mock his taking the 5th. This was the same Hawley who ran frantically to escape the Trump mob of traitors and insurrectionists as they breached the Capitol back on Jan. 6, 2021.
They’d rather use the bogus hearings to disparage Fauci personally, to try to paint a picture of him as having pursued fame and money at Americans’ expense, and mocking him for taking the Fifth Amendment. These same delirious maggots would now likely be pushing up mud had it not been for Fauci's rigorous defense of masking as well as vaccines after Covid struck.
And huge kudos to CBS Medical correspondent Dr. Celine Gounder for ripping an asteroid -size hole in the GOP's phony Covid narrative - while neutering their attacks on Dr. Anthony Fauci.
As more news of the McCarthy-style Senate sham hearing seeps into Americans' awareness, they will surely wonder why these numbnuts and losers ceded more power to Trump in his Iran War in a vote last week. As well as wasting precious Senate time - performing like trained monkeys - to appease their orange Fuhrer.
That as opposed to helping them with ever rising prices in groceries and gas. My bet is that these performative pretenders will pay big time in November, losing BOTH Senate and House. You can make book on it.
See Also:
by Thom Hartmann | August 1, 2026 - 4:57am | permalink
Republicans went totally nutso on Dr. Anthony Fauci this week, trying to catch him with a perjury trap before the US Senate. They called him names, citied lies and pseudoscience, and attacked his integrity.
He withstood asinine statements like Josh Hawley, in an extraordinary bit of projection, saying:
“You became a narcissist and a megalomaniac and a liar! You’ve done more to harm science than anybody in my lifetime!”
Throughout it all, he retained his composure and refused to take any of their bait.
And:
And:
by Amanda Marcotte | July 10, 2021 - 7:37am | permalink
And:
Jon Stewart's 'Lab Leak' Rant On Colbert Confirms He's No Covid Expert (brane-space.blogspot.com)
And:
New Research On Laotian Bats Pokes Final Holes Into Covid Lab Origins Codswallop
And:
by Matthew Rozsa | July 27, 2026 - 5:17am | permalink
President Donald Trump is going to be the main issue in the 2026 midterms, but experts disagree as to whether the impending electoral disaster will be experienced by the Republicans or the Democrats. Now an election expert is shedding light on the situation.
“It’s a competitive situation in both the Senate and the House,” DDHQ’s chief elections analyst Geoffrey Skelley told The Hill's Julia Mueller on Sunday. He later added that “the big question is: will the Iranian conflict … will people being concerned about that ratcheting up, is that going to create reverberations in things like the generic ballot that signal ‘OK, Democrats’ advantage is growing again’?”
"Single particle dynamics" is perhaps
the most important introductory aspect of plasma theory, especially
for space plasmas (e.g. Earth's magnetosphere, heliosphere etc.). Specifically,
it is the domain wherein we enter plasma “orbit theory” and consider a charged
particle (say of charge q) in a uniform and constant magnetic field (B).
The behavior of such charges, in both magnetic and electric fields, is crucial
for understanding plasma behavior as a whole.
The governing equation of motion with F the Lorentz force, is:
m (dv/dt) = q(v X B) = F
The motion here is such that v will always be perpendicular to the force acting on the particle so v ⊥ F, implying circular motion. Thus:
dv/dt = q/ m [v X B]
Meanwhile, (v⊥ ) 2 / r = q/ m [v⊥ B]
The quantity r above is none other than the gyro-radius. Solving for it one finds:
r = m/ q [v⊥ / B] = v⊥ / (qB/m) = v⊥ / Ω
for which one can have either the electron, or ion gyro-frequency (Ω). The ion gyrofrequency will be:
Ω i = qB/ m i
And the electron gyrofrequency is:
Ω e = qB/ m e
These equations help to explain the physical basis for the origin of a preponderance of radio waves (i.e. gyro-magnetic emission) such as from the Sun, and other cosmic objects (e.g. quasars, pulsars).
Note that the velocity v has two components, parallel and perpendicular:
v = v|| + v⊥
where the first term denotes the velocity along B which stays constant so that d(v|| )/ dt = 0.
Further, we have:
v⊥2/ r = q/ m [v⊥ · B]While on this topic it is useful to also consider the "gyration velocity" which is simply the magnitude:
v⊥ = 2 m m B/ m
where m m is the magnetic moment.
Thus, the proton gyrates at this rate provided m m is a constant of the motion: viz. m m = m(v⊥)2/ 2B = const .
The gyro-period is: T = 2 p / Ω
Bear in mind the gyration energy:
E = m m B = m/2 (E/B) 2,
Note that the position of a particle at any time t can always be specified for a given coordinate system, if one knows the Larmor radius r and the gyrofrequency, Ω:
Thus: r(t)= r (cos Ω t x^ - sin Ω t y^)
Which equation can be referenced to the diagram below:
The basics presented above ignore the fact that no general
solution exists to the equations of motion for a charged particle moving under
the influence of the Lorentz force in a dipole B-field.
What happens is that an approximation is needed, called “the guiding center
(GC) approximation”. This assumes the magnetic field changes are
small over a gyroperiod, and gyroradius.
If a charged particle is moving through a converging magnetic field, i.e. a magnetic 'bottle such as shown below:
Then it gyrates in increasingly tighter circles, but the speed of its circular motion increases. The kinetic energy involved in this circular motion also increases but the total kinetic energy remains constant, so the kinetic energy of this circular motion comes at the expense of the particle's forward motion along field lines. The farther the charged particle moves toward one end of a magnetic bottle, the slower it goes in that direction.
Based on this simplification, the electron or ion moves along
B-field referenced to a guiding center, such that:
(a ) x – xo = - i v⊥ exp (i Ω t)/ W = r sin (Ω t)
and
(b) y – yo = ± v⊥ exp (i Ω t)/ W = r cos (Ω t)
The key point is that the guiding center (xo, yo)
is fixed. while r is the "Larmor radius" (or gyroradius).
In the GC approximation, particle motion displays three components:
1) gyration about a field line (given by the gyrofrequency, or
cyclotron frequency);
2) reflection between two mirror points (embodied by the
“bounce period”) and
3) a gradual longitudinal drift, denoted by the (E x
B) drift.
Suggested Problems:
1)Given the situation shown below for a particle in plasma:
And: v o = v xo x^
+ v yo y^ (for initial velocity)
Solve the equation of motion: F = q(E + v
X B)
2) (a)If the perpendicular velocity component ( v⊥) is 105 m/s for
an electron in a plasma, find its Larmor radius, gyration energy and its
gyro-period.
(b) Find the guiding center positions for the electron
referenced in (a) if t = T/2.
Why are soon -to- be graduated astronomy and physics students depressed and uncertain of their futures - or even whether they should go into their chosen fields? The answers have gradually emerged since what scholars call "the pandemic years" - when even university lectures were reduced to Zooms - and many undergrads ended up paying as much tuition for long distance classes as for regular ones.
Two recent (2025) Physics T oday news stories:
Physics, astronomy graduate admissions in the US expected to shrink amid funding uncertainty and
Funding uncertainties muddle graduate admissions .
shed some much needed light on the reasons and especially primary sources of uncertainty. It turns out these areas of angst can be reduced to three main sources:
1) The relentless intrusion of AI and automation into research domains, jeopardizing future employment,
2) Professional-academic employment opportunities cratered by Trump regime's massive funding cuts, i.e. to NASA, physics and astronomy department.
3) On account of serious stress experienced, and academic demands, a compound feeling of "impostor's syndrome" and unease about physics (and astronomy) as viable career paths.
To evaluate the degree and extent of concerns the Society of Physics Students (SPS) and Sigma Pi Sigma, organizations of the American Institute of Physics (AIP, publisher of Physics Today), conducted a survey last year at the Physics and Astronomy Congress at the University of Denver. This has typically been the largest conference for undergraduate physics and astronomy students. Echoing the surveys that had been conducted at the 2016, 2019, and 2022 congresses, the 2025 survey asked undergraduates to identify the two most important issues currently facing students.
The latest survey was completed by 483 students. The first question asked students to identify the two most important issues facing them, their physics and astronomy clubs, and their colleagues. Students couldn’t select more than two.
These turned out to be: (a)the rapid integration of AI and automation into the academic sphere - which we already saw an example of in math when an Open AI model solved the 80-year old Erdos problem, e.g.
Open AI Model Solves 80-Year Old Erdos Problem - And Mathematicians Freak Out
And: (b) Upending of the physics and astronomy labor markets , mainly by the widespread shredding of research support funding. (See links at bottom)
Less noted in earlier meetings, but now a top topic for angst are the academic stresses even at undergrad level which have led some to even consider whether pursuing further advanced degrees is worth it. And this in itself breeding a nascent "impostor syndrome". (The belief one's achievements are exaggerated or 'fake' - in any case one's success is not as real as perceived.) Indeed, many have questioned whether their education has prioritized grades over understanding, applicability and joy.
As for stress, by 2022, students identified burnout as a critical systemic hurdle. For example, one student said, “Students are expected to do internships, REUs [Research Experiences for Undergraduates programs], research, conferences, presentations, et cetera, et cetera, to even have a shot at graduate school or a career". This has been compounded as a consequence of many departments pursuit of unrealistic norms combined with inadequate support and a constant pressure to compete in an increasingly constrained (e.g. by federal funding) system.
Add to that the fact that students are increasingly stressed by the overarching uncertainty of science’s future and the severe competition for a withering number of academic placements, and one can begin to grasp the level of mental health issues faced by physics and astronomy Ph.D. students, as well as undergrads. For an analysis of the mental health issues faced by physics and astronomy PhD students, see the April 2026 Physics Today article “Building graduate programs that support mental well-being ,” by Patrick Banner, Kellen O’Brien, and Chandra Turpen.
One student noted in the 2025 survey, for example, “the feeling that there aren’t enough jobs and that most will be unemployed or forced to work outside the field.”
The fear of having to work outside one's field is clearly justified, given - as many students reported - there is insufficient preparation for pursuing career paths outside of academia. Though most recipients of physical sciences bachelor’s degrees end up in the private sector, students said that they felt unprepared to translate their skills to industry, that they lack career pathway exposure, and that they see graduate school as both the only option and increasingly unattainable.
Such uneasiness about physics and astronomy as viable career paths, combined with unstable funding in the Trump era, not to mention technological disruptions - risks a significant brain drain as students may pivot away from research toward more stable or lucrative majors and roles.
Students overwhelmingly identified unstable funding as a root cause of concern about internships, graduate admissions, and long-term careers, with 31% of respondents selecting research funding among their top two concerns. Many students also stated that they perceive physics as an elite, shrinking field where opportunity depends more on timing or funding than on merit. Which in many cases is absolutely true. After all, widespread reductions in funding for graduate students and basic science have led to shrinking research opportunities, department closings, and a decreasing number of graduate seats.
One student wrote, “I think that as of today many
physics students are worried about finding viable careers. It seems that every
job that a physics major applies to requires a PhD or postdoc, leaving many of
us who desire to enter industry feeling like backup options to engineering or
data science majors.”
Not surprisingly, many respondents also reported that anti-intellectualism is directly threatening the future of science. Well, how can they not be stressed by this when they see it played out nearly every day in this country: from the denials of vaccine efficacy, to the attacks on climate science, and Trump even closing down a critical climate research institute here in Colorado, i.e.
Dismantling Of Premier Climate Research Facility Here in Colorado Will Have Repercussions Worldwide
See Also:
And:
Alas, The U.S. Brain Drain Is Real & Thanks To Dotard Is Becoming The World's Gain
And:
The Real Reasons The Trumpists Are Targeting Scientific Journals
And:
Anti-Intellectualism In The U.S. - A Real Concern Or Hyped Worry?
And:
AAS Press Release expressing concerns about the proposed budget: https://aas.org/press/aas-statement-nasa-cuts
And:
by Henry Giroux | July 27, 2026 - 4:36am | permalink
Across the United States, and increasingly in other democracies under siege, higher education faces a coordinated assault unlike anything witnessed in generations. State governments are prohibiting the teaching of histories that confront slavery, colonialism, Indigenous dispossession, structural racism, and widening inequality.
Books are disappearing from classrooms and libraries. Diversity, equity, and inclusion (DEI) initiatives are being dismantled. Faculty are encountering political intimidation, ideological surveillance, and threats to their employment. Students who have protested Israel’s devastating assault on Gaza have been suspended, arrested, disciplined, and treated less as citizens exercising democratic rights than as enemies of public order. Universities themselves are facing threats of financial retaliation if they refuse to conform to the demands of increasingly authoritarian governments.
