Amr Morsi

That's right.

Also, when the paper is raised enough, it is got affected by the dynamic pressure of the blown air, and it get pushed down again..... That's why it vibrates.

First, I think that F(x) = -q gradΦ(x), not F(x) = -q divΦ(x), is the correct formula.

Second, you have the potential energy of the charge, which when added to the kinetic energy, gives the total energy E, which is a constant. The last equation is function of dr/dt, d(theta)/dt and r. Another equation for theta is

r^2 * d(theta)/dt=constant=a,

this equation is analogous to conservation of angular momentum.

Both differential equations can be solved to find r in terms of t. Try it yourself.

Some experiments have been made, after making the suitable circumistances, to collide two photons and convert them to a pair of electron and proton with the same energy. Such operation can be expected by Quantum Electrodynamics.

You are right ajb. Photons are particles that carry energy (, frequency and phase). By the way, although the rest mass of protons is zero, they do have a motion mass, which is h*(mu)/c^2, where mu is the frequency of the photon.

Why timo? Multiply both sides by [AA]^-1, which gives x=[AA]^-1 . 0=0.

Why not?

Multiply both sides by A from the left and then use the notation you introduced, which is A . vo=0. Then you will have A^2 . x = 0 which gives x=0.

Differentiate with respect to n and equate to zero. And, then find the nearest natural number. Note that x will be considered a constant. Also, I think that n! will be considered constant as differentiation is over a small variation around n.

Do you have a relation D>>E or E>>D? This can be used in an approximation which makes it possible to integrate to a closed form.

What Euclidean Norm and Maxnorm have to do here? You can easily get the limit by substituting with x=1 and y=1, you will get lim f(x,y)=1*1=1.

What is meant by "monotone sequence"?

The only discontinuity is at x=-1, which is not included in the domain (0,infinity). Therefore the function is uniformly continuous in(0,infinity).

It is impossible to have c dimensionless in any system of measurement. It will always be length/time. But sometimes, it is omitted, but, it is known implicitly that any velocity term is divided by c.

Actually, I think that the reason the velocity of light has this value is two points:

1. The system we use for measurement.

2. It is a universal constant, exactly such as pi. Actually, it is composed of 2 universal constants (epsilon and mu; permittivity and permeability)where

c=1/sqrt (epsilon*mu)

What is meant by "gravitational potential energy is gravity source also" is that it is another manifistation (face) of the gravitational energy. The mass of the potential energy is still "M", icarus2.

The only relation connecting it with mc^2 is the following relation, which can be deduced from SR (Special Relativity), neglecting GR effects:

-GMm/r+gamma*mc^2=E

Where E is the total energy of motion of m.

This is equivalent to what swansont is saying.

When cooling a material and then heating it, some parts get heated, and thus expanding, more than others. And, that's why it could break. The more quikly the heating, the more liability to breaking.

Since atoms in one molecule are not moving with respect to each other, then magnetic field will not affect the internal structure of the molecule.

But, since the whole molecule is vibrating, then the magnetic field will make the polarized molecule to rotate, but, will not increase, nor decrease its velocity (because magnetic force is always perpendicular to velocity).

I totally agree with you.

But, what do you mean by "the singularity is a stable form of energy"?

I can find from another question for you, Alejandrito, that you are perfect in calculus, ...... if I didn't misunderstand you.

It is not a must to have a star collapse in order to produce gravitational waves. They can also be produced from 2 masses rotating around each others. In general, gravitational waves are produced from any accelerating mass....... very similar to electromagnetic waves.

It is also to be noted that when a star collapse into a black hole, this doesn't imply a transformation to energy, but it is contraction of mass over space.

By the way, simple spherically-symmetric contraction of stars or expansion doesn't emit gravit. waves, as stated by Einstein.

The R.H.S. of Eq. 2 is only a function in y, the rest are constants. So, differentiate it with respect to y, and then substitute a time with y=0 and another time with y=1/2. You will get 2 relations for the constants a'o and a'1/2 and thus get both in terms of ao.

The same can be done with eq. 3.

Merged post follows:

I think you will have to integrate Eq.1 and T00 with respect to y in order to get rid of the delta function present in T00. Integrate it from -epsilon to +epsilon and thus some term in G00 will vanish and then substitute with the constants-relations you obtained previously.

Merged post follows:

If Eq. 2 is NOT differentiable at y=0, try to integrate the equation following it(containing a''), it is the origin of Eq. 2...... It will be easy to evaluate.

If the potential is not a function of time (i.e. function of space only), then schrodinger equation will be solved by separation of variables, and the time function will be only a phase function (exp(-iE*t/hbar)).

However, if the potential is function of time, then the solution will be more complicated and the maximum of the probability density function will be moving with time through space; which gives the analogy to motion in classical physics.

For the former equation you wrote, integrate both sides and make the boundary conditions -Pi and phi. You will get 1+k*phi=T, i.e. phi=(T-1)/k.

Merged post follows:

Sorry for this error. Make the boudary conditions phi and pi+epsilon. And, you will get 1+k*(pi - phi)=T.

When you use a potential function in time (such as step up or step down) the schrodinger equation may give you a collapsed wave function or a generated one. But, in general, Schrodinger Equation gives stationary states when the potential energy (V) is not function in time, and the solution is obtained by SOV Method.

1. The curl of the static gravitational field will not change with the velocity nor acceleration of the affected body but with those of the source mass, i.e. it will be dynamic gravitational field. This can be solved using General Relativity.

2. B® is solved in the attached file for the example you give, just put acceleration equal to zero. Exact B® is given and then approximation is made. Time retardation effects mean the properties of the charge at the time the radiations reach a position P...... It is not an approximation.

- With respect to radiation; the electron gets accelerated from the external field, and some energy goes to the kinetic energy of the electron (and change in the direction of the velocity) and a small portion goes to the field radiation.

- According to uniformly moving charges frame of reference, the magnetic field will be zero, as the charges will be considered motionless, only there will be electric field.

Gauss's law for magnetism is an associated law (since the right hand side is zero), it helps in adding to the other laws that the magnetis flux lines are continuous.

1. The curl of a static gravitational field is zero

2. To solve the example, thanks to refer to the attached file.

chap14.pdf

But don't forget that ions do contain shells of negative electrons. And that is the reason they remain separated by a certain distance.