Would AC power = VxIxSin Φ be more accurate than Cosine Φ ?

It's Poynting that does the E x H direction of power flow thing (see also Hately Antenna for 'discussions')

One must also consider the three types of polarisation (Horizontal, Vertical & Circular..[*]).

It all gets very 'confused' as one moves from simple Direct Current (DC) currents in wires and resistors, to Low Frequency (LF) Alternating Current (AC) currents, then 'three phase' systems with their vectors, and upward to High Frequency (HF) AC, and onward to radiated field (rf) Radio Frequency (RF) signals which need no wires. 

There is plenty of space for alternate choices, including going full Quaternion (all Maxwells equations embodied in just two equations - references available).

The hard bit is to both simplify the discussion for those getting started, yet be able to highlight that as they gain more broader and deeper knowledge that the simplified discussion can appear wrong in other scenarios (but they don't know enough yet).

[*] Vertical polarisation could be used to show quantum gravity (how does it know it's vertical - see mirrors and reflection..). Circular (C) polarisation can have left (L) and right (R)  polarisations, and if combined can create horizontal (H) or vertical (V) polarisation; or the V & H can be split to produce L & R; "who knew"

Circular polarisation is spin but is directional and can be clock or anti-clock which balances to nothing in a frictionless electromagnetic pendulum in 3D space.

Everything in the whole universe experience spin from largest galaxies to smallest particles. This  spin is provided by magnetism which along with electrostatic repulsion can explain the dark forces that govern and balance up our universe.

circular polarization of an EM wave,  is not anything like what is meant by spin in an atomic or particle physics sense.

Atomic 'spin' is just a measure of the magnetic dipole moment (static magnet strength) of a whole nucleus or of a sub atomic particle or cluster of the same. In the QM sense, the smallest possible value is assigned the value of either + or - 1/2, being either with or against the external field used to detect it.  (one low energy aka 'ground' state, one higher energy, aka 'excited', state where the alignment is the one it does not want to be, and energy has to be put in to get it there.)

The modulus has to be half as zero is not an option for something like a single electron or a proton as it always generates a magnetic dipole field. Obviously a pair of such elementary particles can present a magnetic moment that sums to +/-1 or 0, where of the 4 possible states 0 occurs twice and is therefore more likely in a system at rest.

Mike.

Mike, the circular spin of a EM photon wave is essential to give massless light momentum. That inertia can be absorbed as energy depending on the physical and electrical parameters which change dramatically with frequency.

However, to create a universe from nothing in a big bang, everything must balance electrically thus all positive and negative charges in matter and anti-matter will annihilate if time suddenly stopped.

Err no, not really,  again.  Photons really do not have 'spin' in the sense of atomic or particle physics at all.  

Iron filings are not attracted to light bulbs are they ? They would be if they did.

And in case it is what you meant, EM waves do not have to always be circularly polarised either.

Photons, or if you prefer, the waves whose amplitude represent their spatial extent,do indeed  possess both momentum. and energy in proportion to the frequency,  but have no mass, and they move at speed 'c' in the medium, if there is a medium. 

Fully agree the momentum and the energy are transferred to the target when they illuminate it, and generally  converted to heat, unless something else specific happens, like the generation of photo-electric current.

I'm not at all sure what you meant to say with the 'if time suddenly stopped' comment. It's both incorrect, and a non-sequitur.  

Mike

Mike,

Momentum can exist in the x,y area of space but energy requires a 3D volume of space x,y,z for matter to exist in. 

Google AI states " Poynting  vector represents the directional energy flux density (power per unit area) of an electromagnetic field, with SI units of Watts per square metre.

We need a cubic metre equation with Cosine angle to be correct surely?

I'm sorry but I'm really not too sure what you are saying there either. I think you might be restating a variation on Poisson's equation, or perhaps some sort of continuity expression, To paraphrase,  whats in the box is the amount going in per second minus  the amount going out the other end per second, times the time its been happening in seconds ?

Mike.

Mike.

Mathematics is the problem as it is not 3D specific.

We live in a magnetised spin and electrostatic polarised solar system with dark forces of which gravity attraction G is only 4% according to WMAP result which means a dark energy attractive electrostatic force  of 25G gives the other 96%.

Space.com articles are full of seeing magnetic spin forces of balanced magnoflux flux of 6G all over the universe including the solar system but this cannot be measured

Quantum theorists agree that Plancks constant [h] needs to be reduced by 2 π but is missing the necessity of synchronising the electromagnetic light waves before bringing them together. We need to add Cos or Sin(θ) so we can see how fringing occurs and confirm that 6.24 is the universal magnoflux spin dark matter force constant  

The factor of 2 pi, or not, arises due to the expression of radian frequencies ,and radian wave distances, as opposed to full cycle frequency in Hz (cycles per second ) or full cycle wavelength in metres.

The mains frequency in the UK is 50Hz, which is the same as saying its 314.xx  radians per second .  (Same as in the == sense  -a 3 line equals not in the font sadly, equal by identity, not by coincidentally equal by one time by calculation).

The (full cycle) vacuum wavelength of a 1MHz radio signal is a tad under 300m, the same signal also has a radian wavelength of a touch under 48m, that being the distance over which the delayed potential are 1rad, ~ 57 degrees apart.

This has nothing especially particular to do with quantum mechanics, except for convenience when solving in spherical co-ordinates (for things like energy levels in atoms)  or fields around wires, (circular co-ordinates) factors of pi tend  to crop up a lot, and bundling it with an other constant to save chalk, pen or whatever you are solving it with is standard maths technique.

regards Mike.

The factor of 2 pi, or not, arises due to the expression of radian frequencies ,and radian wave distances, as opposed to full cycle frequency in Hz (cycles per second ) or full cycle wavelength in metres.

The mains frequency in the UK is 50Hz, which is the same as saying its 314.xx  radians per second .  (Same as in the == sense  -a 3 line equals not in the font sadly, equal by identity, not by coincidentally equal by one time by calculation).

The (full cycle) vacuum wavelength of a 1MHz radio signal is a tad under 300m, the same signal also has a radian wavelength of a touch under 48m, that being the distance over which the delayed potential are 1rad, ~ 57 degrees apart.

This has nothing especially particular to do with quantum mechanics, except for convenience when solving in spherical co-ordinates (for things like energy levels in atoms)  or fields around wires, (circular co-ordinates) factors of pi tend  to crop up a lot, and bundling it with an other constant to save chalk, pen or whatever you are solving it with is standard maths technique.

regards Mike.

3 line equals not in the font sadly

One of these? ≡ (just right of centre, 3rd row)

   - Andy.

yes one of those ;-) That'll remind me to check the insert menu from time to time. Time was it was mostly smiley faces. 

Mike

Mike, all the maths is two dimensional basically but to synchronise the third spin angle dimensionally is necessary .