Problem Solving Strategies

@JohnRennie If one little dipole contributes 4 field lines... then 4 such dipoles should have given out 4*4=16 field lines but here we see that we get just twice the field lines....The second row of dipoles doesn't increase the strength....

It is wrong...but I don't get how...sir

John Rennie

You need to be careful about taking field lines too literally. Remember that they don't really exist. They are just a way of showing the direction of the force that would be exerted on an (imaginary) magnetic charge.

It's not safe to add up numbers of fields lines as if they were real objects.

user8718165

@JohnRennie yes sir....what I meant was that more field lines = more strength....but the interior dipoles dont increase the lines....only those on the surface do....the inside ones just complete the loop

@JohnRennie okay

John Rennie

If you had four magnetic dipoles in a vacuum you would just add the four fields (vector addition) to get the total field.

However in this case the dipoles aren't in a vacuum because you have large chunks of ferromagnetic material present with a high permeability.

user8718165

4:34 AM

@JohnRennie okay sir

John Rennie

I'm not sure how you combine the fields when you have high permeability material present. It isn't something I've ever done.

user8718165

oh....I got what you're saying sir

@JohnRennie You say that the internal dipoles increase the field strength (vector addition stuff)...that's just shown by more field lines...we shouldn't take the field lines too seriously...as they just give a rough idea

correct sir?

John Rennie

@user8718165 there isn't a set number of field lines. Any point in space around the magnet has a field line passing through it. So you can draw as many field lines as you want.

We normally choose the spacing between field lines just for clarity. There isn't any fundamental significance to how many field lines we draw.

user8718165

@JohnRennie okay sir...but is there a max. limit on how many lines we can draw...$1 Wb=10^8$ flux lines(maxwell)

John Rennie

No. There isn't a set flux per field line.

Let's go back to electric charges for a moment as it will make my agument simpler.

user8718165

4:44 AM

@JohnRennie okay sir...

John Rennie

Consider a charge Q with a Gaussian sphere around it. Then the field lines are straight lines going outwards from the charge through the sphere.

user8718165

@JohnRennie yes...

John Rennie

If we draw $n$ field lines then each field line is associated with an area of the sphere $4\pi r^2/n$ and the flux corresponding to that field line is the total flux $Q/\epsilon$ divided by $n$.

user8718165

@JohnRennie that's Gauss theorem....right sir

John Rennie

But we typically draw the field lines at some convenient density that makes the diagram clear. So if we increased the charge to $10Q$ we wouldn't draw ten times as many field lines.

We'd probably draw the same number of field lines but now each field line would be associated with ten times as much flux.

My point is that there is no standard flux per field line.

@user8718165 yes, I'm using Gauss' theorem.

user8718165

4:49 AM

@JohnRennie :-)

@JohnRennie got it

@JohnRennie I was confused as I googled 1 wb...It showed me 10^8 lines...

John Rennie

@user8718165 you mean the unit of magnetic field?

Weber (unit)

In physics, the weber (symbol: Wb) is the SI derived unit of magnetic flux. A flux density of one Wb/m2 (one weber per square metre) is one tesla. The weber is named after the German physicist Wilhelm Eduard Weber (1804–1891). == Definition == The weber may be defined in terms of Faraday's law, which relates a changing magnetic flux through a loop to the electric field around the loop. A change in flux of one weber per second will induce an electromotive force of one volt (produce an electric potential difference of one volt across two open-circuited terminals). Officially: The weber is commonly...

user8718165

@JohnRennie yes sir...that's it

John Rennie

One weber is $10^8$ maxwells, but that doesn't mean $10^8$ field lines. A maxwell isn't one field line.

Ah, I see from the Wikipedia article on the maxwell that the unit was originally called the line. That's ... confusing :-)

Maxwell (unit)

The maxwell (symbol: Mx) is the CGS (centimetre-gram-second) unit of magnetic flux (Φ). == History == The unit name honours James Clerk Maxwell, who presented a unified theory of electromagnetism. The maxwell was recommended as a CGS unit at the International Electrical Congress held in 1900 at Paris. This practical unit was previously called a line, reflecting Faraday's conception of the magnetic field as curved lines of magnetic force, which he designated as line of magnetic induction. Kiloline (103 line) and megaline (106 line) were sometimes used because 1 line was very small relative to...

user8718165

@JohnRennie google.com/…

John Rennie

@user8718165 that's because the unit maxwell was originally called the line.

user8718165

4:55 AM

@JohnRennie Got it sir...thanks a lot sir...I thought they meant field lines XD

John Rennie

But that was just a name for the unit. It doesn't mean a field line.

I must admit I didn't know that. But then we normally only use SI units and the maxwell isn't an SI unit.

user8718165

@JohnRennie its cgs....right

@JohnRennie One last doubt...

John Rennie

@user8718165 yes?

user8718165

@JohnRennie Sir we always say a changing B field creates an E field but actually...the oscillating charge does that...right and not the field itself...

John Rennie

It's not as simple as that. For example a light wave has no charge associated with it yet it has oscillating electric and magnetic fields.

In effect the electric and magnetic fields create each other.

user8718165

5:06 AM

@JohnRennie can you please tell me a bit...how

John Rennie

All EM fields are described by Maxwell's equations, and these tell us that a changing magnetic field is associated with an electric field, and also that a changing electric field is associated with a magnetic field.

user8718165

@JohnRennie I used to think that as the frequency of oscillation was increased very very much...you could get light :-/

John Rennie

@user8718165 light is indeed associated with oscillating charge. There is a really nice question and answer about this, though it's probably a bit advanced for you. Let me see if I can find it.

35

Q: Is there oscillating charge in a hydrogen atom?

In another post, I claimed that there was obviously an oscillating charge in a hydrogen atom when you took the superposition of a 1s and a 2p state. One of the respected members of this community (John Rennie) challenged me on this, saying: Why do you say there is an oscillating charge distri...

user8718165

@JohnRennie anyways....transcript is always there...

@JohnRennie these things are QM...right

John Rennie

@user8718165 yes

user8718165

5:16 AM

@JohnRennie I have heard that maxwell's eqns are the most basic...what they say can't be derived from something more basic.Is it actually?

John Rennie

Yes, that is true. Though if you start from special relativity it turns out that Maxwell's equations are the simplest possible equation for describing an electromagnetic field.

So while they can't be derived from a simpler principle they can be justified i.e. they seem natural and kind of obvious when you consider special relativity.

Obviously Maxwell didn't know this because Einstein hadn't even been born when Maxwell wrote down his equations :-)

user8718165

@JohnRennie so a changing B field and E field stuff will seem intuitive when studying GR...right sir?

John Rennie

Yes, though this is heavy stuff. You wouldn't study the covariant formulation of Maxwell's equations until second or third year of a physics degree.

user8718165

@JohnRennie sir...how did he understand it then...

@JohnRennie okay sir

John Rennie

Covariant formulation of classical electromagnetism

The covariant formulation of classical electromagnetism refers to ways of writing the laws of classical electromagnetism (in particular, Maxwell's equations and the Lorentz force) in a form that is manifestly invariant under Lorentz transformations, in the formalism of special relativity using rectilinear inertial coordinate systems. These expressions both make it simple to prove that the laws of classical electromagnetism take the same form in any inertial coordinate system, and also provide a way to translate the fields and forces from one frame to another. However, this is not as general as...

@user8718165 there were lots of laws known that were experimental observations e.g. Ampere's law, Faraday's law and Gauss's law.

Maxwell's genius was to realise that these were special cases of the equations we now call Maxwell's equations.

So Maxwell arrived at his laws by trying to unify lots of different experimental observations using a single set of equations.

user8718165

5:23 AM

@JohnRennie yes sir...got it...

@JohnRennie Thanks a lot sir...That's all...hope won't get stuck anymore today...XD

user8718165

6:20 AM

Hii @JohnRennie sir

John Rennie

@user8718165 I'm working now for about half an hour

user8718165

@JohnRennie that's fine sir

user8718165

12:28 PM

hii @Chris

welcome to pss room

Chris

@user8718165 Hi. I wasn't actually aware I was in this room at the moment, so your ping surprised me ;)

user8718165

@Chris :-)

ROBIN RAJ

7:25 PM

$\ a\lvert\alpha\rangle =\alpha\lvert\alpha\rangle$
Where $a$ is the annihilation operator mentioned in algebraic method of harmonic oscillator ,$a\lvert n\rangle = \sqrt n\lvert n-1\rangle$
Suppose we can express $ \lvert\alpha\rangle $
as

$\lvert\alpha\rangle =\sum_{n=0}^\infty c_n\lvert n\rangle $ then what is the value of $c_0$ ?

physics.stackexchange.com/questions/488116/… please check this link and its comments, what is your suggestion

Transcript for

Problem Solving Strategies