darkenlighten

I'm going to give this one more shot. Please read this with unbiased attention first and the speculate.

I tried to explain and you thought it was semantics. 1st and 2nd equation are to be used on a single E and B field (single charge/electron), so 1st equation supposedly can be derived in "half" the Coulomb's law, which will evaluate electric field potential in relation to its own source and not related to anything else, no interaction, no induction here - NO FORCE. Similarly, 2nd equation is supposed to be equivalent with Biot-Savart law, but it's obviously not.

Okay so the 1st equation allows you to find the electric field of a source, including point, lines, surface and volumes charges. And you can use superposition to get the whole story of the other electric fields from other sources, in which you can then use F = qE, where E is the sum of all fields.

The second equation, and I stress, is not what is used to find the B field without boundary conditions, once again it is Ampere's Law you use to find the B field of a source.

3rd and 4th equation are used when what you say the field is "given", which means ANOTHER spatially separate field is there too, at least one more charge/electron, so to have RELATIVE POTENTIAL DIFFERENCE, which leads to attraction/repulsion and movement. Therefore, 3rd equation is supposed to get two halves of the Coulomb's law which then gives us Coulomb's FORCE equation where we have TWO E fields - Q1 and Q2, not any B fields, but 3rd equation is obviously different and that is not how Coulomb's force works, Coulomb's force works like Coulomb's force law says it works. Finally, 4th equation is supposed to be something like Lorentz FORCE equation, where there are actually two B fields - B1 and B2, which it is lacking, as well as geometry and precision, it can hardly describe magnetic force at all. Gravity fields interact only with gravity fields, electric with electric and magnetic with other magnetic fields - no force between two different kinds of fields.

No not all. The 3rd equation is Faraday's Law, which is about induction of the changing B field, creating an E field. And this B field can be solved for using Ampere's Law. Then this E field can be then added to say a source charge with its own E field, so you would have E(total) = E(source) + E(induced), where E(source) can be a sum of multiple sources.

*** INDIVIDUAL POTENTIALS RELATIVE TO ITS OWN SOURCE

1. Gauss's law: divE= p/e0

(SHOULD boil down to Coulomb's law: E= q/r^2

Okay but the point is Gauss's law its much simpler for pretty much everything past a point charge.

2. Gauss's law for magnetism: divB= 0

(SHOULD boil down to Biot-Savart law: B= q*v x 1/r^2

Once again not the correlation to Biot-Savart Law.

*** INTERACTION/INDUCTION of at least TWO FIELDS -> F O R C E

 

3. Maxwell–Faraday equation: rotE= - dB/dt

(SHOULD boil down to Coulomb's FORCE equation: F= Q1*Q2/r^2 (F= E1*E2/r^2)

 

4. Ampère's circuital law: rotB= J + dE/dt

(SHOULD boil down to Lorentz FORCE equation: F(1-2)= q1(v1 x B2) & F(2-1)= q2(v2 x B1)

The 4th equation does not mean only induction, but is the correction of induction to the B field. Hopefully you can understand that ∇ x B = μoJ is the what is used to find the B field and (μoεo)dE/dt is the additional induction from an external changing E field.

So with all of these equations and F = q(E + v x B) you have pretty much everything you need to solve any non-relativistic electrodynamics problem.

And of course you can have a time-varying field, what do you think an EM wave is? And that is how induction works, something has to be changing with time. So in your gravity field example, gravity is, of course, the same at a specific point and changes with respect to distance, but it is the shuttle that is moving which causes the "time-varying field", I understand what you mean there. Same thing with induction can happen, but! You can also have a varying current (AC) which will change the field with respect to time and nothing in the system, besides the current, has to move for this to happen. For example a wire with a charged sphere near by, if the current is varying through the wire, the charged sphere does not have to be moving in order to feel the effect of the changing B field.

So, we have this important law for magnetism that is not used to solve for the magnetic fields? What then, what is it used for? -- You are giving me that equation for LOOPS, again?!? "No, no, no" to you. There is no induction in our example, there is only one charge/electron there. Are you suggesting the change in electron's own B field induces changes in its own E field, and the other way around?

Once again on the loop thing, the loop is describing the area in which a current is passing through the loop, this is the flux that the loop is feeling, which described the B field of the object in question. Similar to the Gaussian surface, where you have a certain charge enclosed in the surface, you have a certain current passing through this Amperian loop. The Amperian loop is not describing your object that you are looking at, but it is describing the the flux of current of that object in that area.

And as I stated above, the 4th equation is not just about induction, but about the whole story of the B field. It could almost be two separate equations. One for deriving the B field (∇ x B1 = μoJ) and one for the additional effect of a changing E field (∇ x B2 = (μoεo)dE/dt), where the total B field is B(total) = B1 + B2.

Is that any better?

Okay so for one, I already solved your problem for the electric field. And I posted the pages so that you would trust my words were just not me talking, but so that I had a legit source. And as I already stated, for this example using Ampere's Law is not the best, nor is it going to be clean. It is best in this situation to use Biot-Savart Law. Which I have posted, the answer you have is an approximation. If you are to read the derivation I posted you would understand why.

I might not know everything about Electrodynamics, but I do know what I have been talking about.

And for finding magnetic fields, you don't use "Gauss's Law for magnetism" as you like to say, you use Ampere's law. As I said before Biot-Savart and Ampere's law only whole true for steady currents. So anything that has symmetry and a steady current is easily calculated by Ampere's Law, say a coaxial cable or concentric spherical shells, anything (like I said before) with spherical, cylindrical or planar symmetry.

I'm out of town right now, so I'll try to solve it using Ampere's Law when I get a chance, but I don't think it'll be that easy considering its not meant for that.

Merged post follows:

How would you know that from "divB=0"? That equation is seriously missing any information about velocity, about magnetic constant, and about the amount of electric charge. Please try to apply whatever equation you are talking about and see if what you said is actually what equation says.

 

Awww, you mean it's useless on its own? Ok, that leaves us with 3rd and 4th equation. -- Can you point any scenario or practical setup that can be solved with only 3rd equation - Faraday's law of induction? Can you point any example or experiment where we can use these equations in differential form?

No, no no....what he means is that "divB=0" is not what you use to solve for the magnetic field, pay attention and read back through, it is the ∇ x B = μoI ⇒ ∫B·dl = μoI(enclosed), not ∇·B = 0

ambros I still think you are confusing the fact that you should get to the same answer with either Maxwell's equations (which include Gauss's, Faraday's and Ampere's with Maxwell's corrections Laws) or Coulomb's and Biot-Savart Law.

And with Ampere's Law, you saying it is only gives loops, but what it is saying is more like the flux through that loops (current) and this why Ampere's law and Biot-Savart law are only applicable for steady currents.

You can give the full 3-d picture with Ampere's Law. I really don't think you will understand their full power until you either take an Electrodynamics course or read a book on it front to back. Go to a local Barnes and Nobles or what have you and look through an Electrodynamics book, the emphasis will not be on Coulumb's or Biot-Savart Laws, but on all the others.

What is that for? I am offering you a demonstration, so to resolve this argument with practical scenario and real world measurements. You were supposed to give some experimental setup that can be solved with Maxwell's equations and where you believe Coulomb and Biot-Savart laws are just approximations so I can prove otherwise.

Edit: That was to show you why B = (μo/4π) * (q v x r) / r^2 is just an approximation for a moving charge if you look at the math I have given you. I'm starting to lose confidence in your math though since you are still not getting it. I mean you should be able to plug in the numbers and or even just look and see how the exact E and B Fields derived here will be different than the approximation. I'm not trying to argue with you, I'm just trying to show you why I am right.

You ended up with Coulomb's law, which Wikipedia and other people here confirmed is not really possible. It also makes no sense to have a set of equations and all you can do with them is derivation to get some other formulas that by some magic incorporate completely different relations. The question here is about applicability of Maxwell's equations and I am yet to see any direct numerical result come out of them at all.

Stop reading Wikipedia, because that is just wrong. Of course you will end up with the same field! Otherwise Gauss's Law would be wrong and well of course it's not. And its not my some magic, its math...Do you not understand that Gauss's Law will give you the same E field that Coulomb's Law will, that's the idea.

What approximation are you talking about? The only approximation in the whole story comes from wires, integrals and the unit of Ampere. It is no approximation if you know positions and velocity vectors, approximation is when you say: -"around 6.242 × 10^18 electrons passing a given point each second constitutes one ampere."

The approximation I am talking is the above one that you ignored since you believed it had no relevance, so please look again. And I never gave an approximation, the equation I solved for the wire is the EXACT field you would experience for that scenario. Do I really need to solve other scenarios for you to understand its not just for wires. You do need symmetry in the problem, but any that is Spherically, Cylindrically or Planar Symmetrical can be easily solved by Gauss's and Ampere's Law, which are apart of Maxwell's equations.

But the approximation is really an aside and is not going to make or break everything else we are talking about.

And it gets worse. You see, amperes do not really tell you the VELOCITY of electrons, which is the most important variable in regards to the magnitude of B field. This definition, and so automatically Maxwell's equations too, are oblivious to different properties of different materials. The same current (amperes) WILL NOT produce the B field of the same magnitude in different conductors, because the speed and amount of moving charges will be different. -- Are you really trying to tell me:

 

divB=0 --> B= k*qv x 1/r^2 ?

 

Where is magnetic constant, charge and *velocity* in Gauss's law for magnetism? Most obviously, do you not see these two equations are opposite and contradict one another? Gauss says: "divB=0", but Biot-Savart describes: divB!=0, so whom do you chose to believe - the first equation that is approximated with line integrals and amperes, that can not even produce any numerical results on its own, or equation that actually gives results and is used in practice as it can describe this field with not just wires and electric currents, but also per point charge (maximum resolution).

The equation is not ∇ · B = 0 in order to solve for the B field it is ∇ x B = μoI ⇒ ∫B·dl = μoI(enclosed) and you can easily derive the same resulting B field with this method. And as you can see ∇ · B = 0 is always zero, because the divergence of a curl is always zero.

Ok, I'll leave semantics alone and concentrate on more practical issues.

 

 

1.) Biot-Savart is a fine enough approximation, its just not completely accurate.

 

- I say it has maximum accuracy in regards to any real world experimental measurements you can find. Please bring on some practical scenario so we can plug in some numbers and I will try to demonstrate.

 

Here is the derivation:

2.) Maxwell's equations can evaluate the E and B field of a point like charge.

 

- Please demonstrate: electron is moving along x-axis at 25m/s, what is the magnitude of its electric and magnetic field potential in arbitrary direction at distance 'r'. No need to do derivation, just say what equations did you start with and write down what is the final expression for E and B.

 

Can you demonstrate by solving the problem above?

 

Would you say gravity field has curl? If you forget about Maxwell's equations and consider everything else you know about electric fields, electrons and their charge - would you say electric fields have any rotation (curl) and can this curl ever change?

I already solved for the E-Field above using Gauss's Law. To solve for B field is the same method, and for approximation it will be the same results we have already discussed.

Your phrasing is wrong, which makes what you say ambiguous. Current (motion) is what is induced, E fields are there before and after with their fields unchanged. What changes is relative position and hence RELATIVE electric potential, not the potential of their own electric fields. E field is not "around" electron, it's what electron is and what does not change, it's what defines its charge and all the rest of its electric properties.

No. Electrons have a charge and electric field, but it is not its charge or electric field, they are not one in the same, see http://www.scienceforums.net/forum/showthread.php?t=46717

The "q" symbol in these equations I can call "charge", "electron" or "electric field", and you should know exactly what is it I'm talking about, it can not be anything else because that's what electron is, there is nothing more to it.

If you say this you are incorrect, q is not an electron, nor is it an electric field. I don't know why you would insist on this.

What part of "simply wrong" did convince you?

 

Please pick some example so I can demonstrate.

 

I have analyzed that, "retarded time" error can not be experimentally confirmed, which directly implies this correction is absolutely unnecessary as we would not be able to verify the difference anyway, but if there is such experiment please let me know. The other thing is that we can always look at these fields from their reference frame, where they are stationary, right?

B = (μo/4π) * (q v x r) / r^2 is a fine enough approximation, its just not completely accurate.

Yes, but I'm saying it is the only way, not just easiest. Maxwell's equations are about WIRES, because of that they lack one whole dimension, behind and in front of the charge.

Maxwell's equations are not about just wires, they can evaluate the E and B field of a point like charge, a surface, and a volume of any type. I'm sorry you are wrong on this. And I'll state again, Maxwell's equations are derived from Coloumb's and Biot-Savart Law.

I think for you to really understand what is going on you would need to take an Electrodynamics course. Griffiths "Introduction to Electrodynamics" is a really good book if you can get it or buy it.

I agree, Solidworks COSMOS and Unigraphics NX with Nastran are really good programs for FEA. Solidworks might be easier to get a hold of, since Unigraphics is a more high end program (for example GM uses this).

If you have any questions about these, I am pretty familiar with COSMOS and really familiar with Nastran.

Seems like you are asking if a negatively charged atom/molecule can be repelled by a positively charged atom/molecule. The answer would be no, they would attract.

I'm talking about Biot-Savart for point particles. Ok, I understand why you disagree, but I can demonstrate, I think. Do you want to come up with some scenario, or would you prefer to see if I can indeed reconstruct the virtual experiment for the unit of "Ampere" and reproduce the results with two parallel virtual wires made only of one electron each?

And so am I...

I do not think your phrasing actually represents what Maxwell's equations are saying, let me correct:

 

WRONG:

- Changing B field WILL create an E field

 

CORRECT:

- Changing B field MAY create a difference in E potential - induce current

(moving magnet around *straight* wire will hardly induce any current)

 

Fields can not be created, that's like saying electrons get created. Charge, electron and electric field is one and the same thing if you look at point particles, there is no electron that is not electric charge which is not electric field, in these equations simply "q". Electron is fundamental particle, the smallest amount of charge (electric field) that can exist, it can not change, disappear or be created in these experiments.

No, a changing Magnetic Field will induce an Electric Field. And no the charge, electron and electric fields are not one in the same when it comes to point particles. They exist because of each other but not one in the same.

Coulomb's law: E = k * q/r^2

Biot-Savart law: B = k * qv x 1/r^2

 

Anyhow, what I'm saying is wrong as much as these two equations are wrong, I'm just saying what I read from them. Do you see any relation of E field with the B field in Coulomb's law? That's what I said, but it is still not generally in disagreement with 3rd Maxwell's equation as I explained above B can indeed create electric potential by displacing other electrons and hence creating electric current. What I'm saying is that B field can not create any new E field/electron/charge.

I'm glad you said this, take a look:

This is taken from the "Introduction to Electrodynamics" (Third Edition) by David J. Griffiths

rotE= - dB/dt

 

Imagine these are two electrons, we are trying to figure out how E of one electron changes as it passes through the dB of the other electron. Do you think this magnetic field can change distribution or the amount of electric charge single electron carry? Do you not agree potential of an electric field is "radial" and that it has no rotation, so do you really think the change in magnitude potential in this magnetic field can indeed make any changes about *rotation* (curl) of the electric field? But most obviously, if electric fields have constant and zero rotation than this equation simply "does not compute".

So you are asking if a changing Magnetic Field of an electron would change another electrons charge??? Because it would only change the E field around the electron, not the properties of the electron itself. This goes back to what you were trying to say about it being one in the same. To change the E Field around an electron does not constitute a change in the electron's properties.

Hopefully you are starting to understand something of what I am saying.

Merged post follows:

Note that B = (μo/4π) * (q v x r) / r^2 is an alright approximation for v^2 << c^2, but is nonetheless not the exact answer. I am not sure how accurate you wanted to be with this.

And I'm just going to add in here to make it clear, for point like particles, Coloumb's Law and Biot-Savart Law is probably going to be the easiest way to get the E and B field. I just want to make sure we were not ever arguing that.

By definition of the Biot-Savart Law, you need steady currents in order for it to be correct. What you have for a single charge is incorrect. You need steady currents and a single charge moving is not a steady current, unless it is in circular motion like an electron "orbit" and then you need the current and not qv.

And I didn't solve for a B field because it is the exact same method as solving for an E field using Guass's Law, but with Amperian Loops (line integrals).

It doesn't have to be infinite wires, that was just the easiest example, it can solve finite solutions.

And of course it will come out the same as Coloumb's and Biot-Savart Law, otherwise it would be incorrect...And Maxwell's Equations were derived from Coloumb's and Biot-Savart Laws, but they make finding the E and B field so much easier.

What is this about there is no way a B field can create an E field??? That is wrong, it has to be changing, but a changing B field WILL create an E field, that is what the Maxwell-Faraday Equation states.

Yea I'm going to have to disagree with you also and be stern that you are wrong. At least in your method of thinking about this...

Okay so point like charges, it is usually best to use Coloumb's Law and the Biot-Savart Law, but for everything else it is probably not true. Guass's Law and Ampere's law make things so much more simpler when it comes to everything else.

And yes you can use the laws in differential form, but you would need to know the E or B before hand. Here is an example:

So for inside it would be different because the charge enclosed would be different. And Guass and Ampere's Law call for symmetry.

The Biot-Savart Law only holds for steady currents, so one electron moving will not be accurately depicted by the Biot-Savart Law, nor can you really with Ampere's Law.

Are you actually saying these equations can not be used before we apply stokes theorem, gaussian surfaces and get them in integral form first? So, the 3rd equation defines dB/dt with 4th equation, and then 4th equation defines dE/dt with 3rd equation, is that not self-referencing and circular definition? EXAMPLE: - electron is moving along x-axis at 25m/s, what is the magnitude of its electric and magnetic field potential in arbitrary direction at distance 'r'.

I am saying you cannot solve for E or B without applying Stoke's Theorem. You can use it in differential form if you already have E or B but that will obviously not solve for either. You might be able to use it to find E and B but I cannot think of anyway off hand. And the dB/dt and dE/dt are external known fields one way or another.

Also for your moving electron and the E field:

TO BE MORE SPECIFIC:

 

1. Gauss's law: divE= p/e0

 

- When do we use this equation? How to get rid of the divergence operator so to solve for just E, and would that be a vector or scalar quantity? Divergence of E field according to Coulomb's law is zero, it has uniform magnitude gradient dropping off with inverse square law, does that not mean divE=0?

So for this, you would use this when you are looking at something with a charge to find the electric field around it. You want to apply stokes theorem to get it into integral form. From there you would take a gaussian surface around the object enclosed in order to get the electric field at a distance away from the object.

So ∇·E = Q/εo ⇒ ∫E·nda = Q(enclosed)/εo

If you have more questions about this I can expand.

2. Gauss's law for magnetism: divB= 0

 

- According to Biot-Savart law which actually describes this magnetic field potential for point charges, *not wires*, this field is toroidal, its magnitude falls off with inverse square law in perpendicular plane to velocity vector (current direction), but it also falls with the angle according to vector cross product, so at the end it looks like doughnut (toroid/torus) and not like a "ball" of an electric field. This actually means that divergence of this particular magnetic field 'due to moving charge' (this is not intrinsic magnetic dipole moment), has non zero divergence and non zero rotation (curl).

 

Yes, if you take an infinite wire then divB=0, but that does not say anything about individual fields, it is very specific case that does not reveal anything about how individual magnetic fields look in front and behind that 90 degree plane, it is very crude approximation and hence lacks information. -- Let's say divB=0, then what is just B equal to? I do not see any information about B field here, so where and when do we ever use this equation?

 

Okay so here you can find the magnetic field using amperes law which is similar to guass's law, which is ∇ x B = μoI, or get the integral form. so you would, for a wire, apply an amperian loop around the wire and take the line integral and set it equal to μoI, where I is the current enclosed.

∇ x B = μoI ⇒ ∫B·dl = μoI(enclosed)

Once again ask further if you want more info.

 

3. Maxwell–Faraday equation: rotE= - dB/dt

 

- According to Coulomb's law E field has no rotation (curl), it is more of a "radial" kind of thing, so what in the world can this mean if we get rid of the curl operator and solve for just E? How can 'curl of E' tell us anything if 'curl of E' is always supposed to be constant and zero?

 

What does "dB" refer to?

a.) to second equation: rotE= - (divB= 0)/dt ?

b.) to fourth equation: rotE= - (rotB= J + dE/dt)/dt ?

c.) to Biot-Savart law: rotE= - (B= k qv x 1/r^2)/dt ?

d.) something else?

Here dB/dt is the derivative of the magnetic field, or the change in magnetic field. You can find B from Ampere's Law. So this is an induced electric field from a change in the magnetic field, once again apply stokes theorem to get it in integral form.

4. Ampère's circuital law: rotB= J + dE/dt

 

- What do we get when we get rid of the curl, how to do it, and what just B then equals to? What J equals to? What "dE" refers to, 1st equation, 3rd equation, Coulomb's law? Are these equations for just one field or do they require at least two like Coulomb's law has Q1 and Q2 and Newton's gravity has M1 and M2?

 

Does rotB, J and dE refer to the fields (potential difference) of one and the same particle, or rotB refers to one field and dE to separate another field? And also, 3rd and 4th equations appear to be kind of 'circular definition' and self-referencing, but hopefully answers to previous question will explain this.

 

In addition, what is the full and exact meaning of "changing electric field causes... B" or "varying magnetic field produces... E". How can E or B field vary if you look at only one charge (electron) or two? Can E potential of individual charges actually change and can there be a creation of any new magnetic or electric potential (new fields)?

 

Thank you.

Lastly I already gave Amperes law above and the dE/dt is maxwells correction and isnt always needed, especially if there is not a change in the electric field. and J is the volume charge, so I = ∫J·da

There for you can clearly see that these will work for wires and most likely for what you were trying to do. If you want me to show you how to do specific scenario please ask. Like how you would get a magnetic field around a wire with current I or something like that.

It's the time evolution of a system. Or how a system behaves given a certain hamiltonian (an equation describing its energy)

I would suggest looking at http://en.wikipedia.org/wiki/Wave_function and asking questions from there. And so we know at least what knowledge level you are coming from.

I'm pretty sure you can just turn off the car. Most cars will not let you switch the key all the way off, but to the point where the cars controller will shut off and any car powering devices. Of course I would suggest attempting to put it into neutral first.

The only way that the electronic throttle control will go haywire would be a error in its control strategy (the electrical signals that get sent to the actual device), which is why the car should be recalled. Or a short in the actual electrical wiring, which is unlikely, but can also happen, causing what is supposed to be a potentiometer, to be a resistance that corresponds to a certain acceleration read by the controller.

But, nonetheless, there are usually manual methods around this.

Depending on the performance of the solar cell, you would connect it as if it was a battery. Otherwise you might need to use it to charge a battery.

It's either going to sustain enough electricity to power it completely (doubtful) or allow the use of a battery to last longer.

So it would help if we knew what you were working with.

I'm attempting to find a mathematical approach instead of an experimental. Also the type of interactions I would like to calculate are not going to be direct repulsion. Knowing the magnetic fields are not the problem, that's the easier part, knowing how they would interact is what I'm trying to find.

Thanks for the input.

Sorry for the delayed response. So from looking at these, they seem to be for a more specific case. Do you know of a more general approach, it does say it is more difficult to find for a general case, but it would be worth learning about.

Okay so I've been wondering if there is a way to calculate the force on a magnetic material (that is magnetized and producing a magnetic field of its own) from an electromagnet that produces its own field.

This is not a trick question or anything of the sort and I've been trying to find detail on this, but I have failed to find how one B interacts with the material of another producing its own field. This question comes about to me when thinking of an electric motor and the force produced by an electromagnet on a permanent magnet.

Does anyone have any insight?

As far as I know, there isn't a specific name for this. Its simply just absorption and emission of photons by an electron. When an electron goes from a lower energy level to higher one, a photon was absorbed, when it goes from a higher energy level to a lower one a photon is emitted.

Yea my parents contributed $0 towards my living and tuition. FASFA and work a part time job. No excuses imo.

Yea I agree with vordhosbn, the logic you are using is still weak. Though, I'm not arguing your idea. Even though I do think that sometimes the consciousness is something past the physical, but I have no evidence to back it up. And I'm not really too sure about it being in "another dimension".

The problems with this hypothesis is that people with damaged brains will report that they are experiencing internal problems with their thinking, not just sensory ones.

 

Brain damage and the above provide excellent evidence that consciousness is brain-based.

I disagree with your logic here. Just because a person is brain damaged and has been disabled to perform the lost function, does not constitute the origin of that function, just that the link is broken or the path to the origin has been broken.

Should have went for Engineering Physics and concentrated in Electrical Engineering like I am Pretty interesting, its not as a popular choice in colleges, but The Ohio State University offers it. And here is ranking in the US for graduate schools:

http://grad-schools.usnews.rankingsandreviews.com/best-graduate-schools/top-physics-schools/rankings

Also an electron is made up of a quark and anti-quark: a Down quark and an Anti Up quark. The Down quark has a charge of -1/3 (e), where e is the charge of an electron (in absolute value) and the Anti Up quark has a charge of -2/3 (e), giving you -1 (e).

And P = E/c and E = hc/lambda, where lambda is the wavelength of the photon of light, so plug in the values and you will get the answer.

Also, F = (k * Q*Q')/r^2 r and the electric field is F = Q E, so Q' does not mean its an electron or whatever, its the value of charge of the particle you are talking about. This is usually also for point like charges. So for the case of an electron it has a certain charge (e) you plug that in for the value of Q' and Q is the "test charge" at which you are looking at the electric field.

I see. The initial state is not known until time has elapsed, of course a very small time. So I believe the second input you are talking about that the NAND Gates are receiving at t = 0 is just a logic 0 or 0 volts, until time has elapsed and it is receiving the desired input/output combination.

And even though this seems like a non-casual system (a system that does depend on an input at t greater than your current t), it does not change once the inputs are set. You are really only getting a delay, which you will learn more about in labs hopefully, though an easy idea to consider due to physical restrictions.