Problem Solving Strategies

@JohnRennie I have a few questions to ask , ping me when you're free.

@Tanuj now is fine :-)

9:14 AM

okay

I have to take my mother shopping in half an hour and for now I'm just killing time.

... and drinking coffee :-)

Woah , that's violent

I hates when my mother goes to shopping

@Akash.B S'OK - she's mainly buying food for my dinner! :-)

@JohnRennie I hates when she is buying clothes

9:18 AM

@JohnRennie I'm taking the picture of the question , just a minute.

@Tanuj I would guess you're supposed to treat them as dipoles, and you need to find the force between the two dipoles.

Okay , so what I understand from this , magnetic fields would be perpendicular ,

@JohnRennie Ah , okay.

@JohnRennie but why would they be applying torque on one another ?

That's why they say the radius is small i.e. it's small enugh that it's a good approximation to treat it as a pure dipole.

@JohnRennie damn

@Tanuj suppose you have two dipoles. I'll draw a quick picture ...

9:22 AM

ok

Is it over Tanuj?

hmm , got it .

@JohnRennie let me try it again.

9:25 AM

Imagine they are electric dipoles rather than magnetic (because that's probably more familiar). Then the two positive ends will repel, and positive and negative ends will attrcat.

@Akash.B yea , for the time being , you can ask @JohnRennie what you want to .

@JohnRennie Is there is any capacitance at the point A ?

@Akash.B is that a battery or a capacitor at the bottom of the circuit?

@JohnRennie It is a battery

a capacitor of infinite resistance

9:28 AM

@Akash.B OK, so there is a voltage across the gap at A.

The answer is that pretty much everything has a non-zero capacitance, but that capacitance is usually negligibly small.

If you had parallel plates at the gap then you'd obviously have a capacitance given by the parallel plate capacitor equation.

@JohnRennie Okay I got it

If you now imagine reducing the area of the plates then the capacitance falls as you decrease the area.

But the ends of the wire have some area, so the area doesn't go to zero and neither does the capacitance.

@JohnRennie Why does the polarity of the ac always change ?

@Akash.B it depends what you're asking ...

@JohnRennie I didn't understand

9:32 AM

The AC electricity is generated at your local power station, and the power station is designed to produce electricity that changes polarity at 50Hz.

So the electricity changes polarity because the generator is designed that way.

The reason AC is used is because with AC the voltage can easily be changed using transformers.

With DC there is no easy way to change the voltage.

@JohnRennie How they are able to design the generator like that way?

Actually it's easier to generate AC than it is to generate DC. If you have a coil rotating in a magnetic field it automatically produces AC. You need a commutator to turn it into DC.

Commutator (electric)

A commutator is a rotary electrical switch in certain types of electric motors and electrical generators that periodically reverses the current direction between the rotor and the external circuit. It consists of a cylinder composed of multiple metal contact segments on the rotating armature of the machine. Two or more electrical contacts called "brushes" made of a soft conductive material like carbon press against the commutator, making sliding contact with successive segments of the commutator as it rotates. The windings (coils of wire) on the armature are connected to the commutator segments...

the power station is designed to produce electricity that changes polarity at 50Hz.So can we produce electricity at 60 Hz ?if so how?

The AC frequency is the rotational frequency of the generator. To produce electricity at 60Hz instead of 50Hz just run your generators faster.

@JohnRennie Okay Thank you

There is an another question

How did Einstein' famous equation helped in the production of atomic bombs?

9:40 AM

@Akash.B it didn't really.

Einstein's theory of special relativity showed that matter and energy are equivalent, though the description of exactly how they are equivalent had to wait for the development of quantum field theory.

The atomic bomb relies on the conversion of matter to energy to provide the BANG, but the development was a lot more complicated than just knowing that E=mc^2.

@JohnRennie But the book told me that "Einstein is lover of non violence and use to hate war and he did not want others to use his equation for that

@Akash.B Einstein was a complicated person, just like all of us really.

He wrote the letter that triggered the development of the atom bomb, or rather he just signed the letter that someone else wrote.

@JohnRennie Complicated person?

They got him to sign it because he was famous and they felt his views would carry some weight.

@Akash.B the point is that after WW2 Einstein regretted his part in the development of the atomic bomb, but before the year he was involved in its development.

So it isn't as simple as Einstein is lover of non violence

@JohnRennie uhm , what exactly is the formula for the force between two dipoles ?

9:48 AM

Which trait is more suitable for a theoretical physicist ?Is it patience or curiosity?

Q: Force between two point dipoles

2

What would the force between two parallel point dipoles be? I was thinking of doing it the way force between two point charges is found out, by finding the field and then the force but I am not able to formulate it.

@JohnRennie I don't even get what it means .

Force between magnets

Magnets exert forces and torques on each other due to the rules of electromagnetism. The forces of attraction field of magnets are due to microscopic currents of electrically charged electrons orbiting nuclei and the intrinsic magnetism of fundamental particles (such as electrons) that make up the material. Both of these are modeled quite well as tiny loops of current called magnetic dipoles that produce their own magnetic field and are affected by external magnetic fields. The most elementary force between magnets, therefore, is the magnetic dipole–dipole interaction. If all of the magnetic dipoles...

under force between two magnetic poles , there is a formula

@JohnRennie oh wait , I just got the answer !

This is pretty much your problem

I have to go now - shopping awaits ...

@JohnRennie thanks , have fun ! :)

@Tanuj Is he gone for shopping?

9:56 AM

@Akash.B Yea , I can see him , he just sat in the car

@Akash.B jk , he must have if he said so :)

@Tanuj How you see him?

@Akash.B I was joking. He must have gone for sure if he said so.

@Tanuj Very funny

@Akash.B no actually , you asking me about him going to shopping was hillarious !

I'm here for a few seconds more while Mum is getting ready ...

10:04 AM

@Tanuj Why your having so interest in mathematics ?

@JohnRennie my exam are starting,any tips?

@Akash.B Relax

@Akash.B Who told you ?

@Tanuj I saw it in your profile are you the member of mathematics community?

@Akash.B yeah , because I have to clear my doubts regarding the subject , I haven't even studied the real mathematics , just high school stuff. Okay I gotta go now. Bye

@JohnRennie How can I stay relaxed?

@Tanuj bye

Ultra Instincts

10:19 AM

@JohnRennie ... Hope you will help me in this topic which I'm clearly misunderstood ... The words are confusing . Can you interpret it more easily ? superposition theorem

en.m.wikipedia.org/wiki/Superposition_theorem

10:37 AM

postimg.org/image/w9j3lkzzr/d2bef98c

Can anyone please explain the graph of 2s and 2p orbital here? Is there any logic in it or is it just factual? Can we relate its dumbbell/spherical shape to its graph? Cc @JohnRennie please have a look when you are back

Also, why does the graph of psi² for 2s orbital have two maximas instead of only one?

@GaurangTandon Can you upload a better picture please?

Not able to see.

10:57 AM

@Abcd postimg.org/image/jxg7859l3 see this is ok?

@GaurangTandon Okay, what's the problem you are facing?

23 mins ago, by Gaurang Tandon

Can anyone please explain the graph of 2s and 2p orbital here? Is there any logic in it or is it just factual? Can we relate its dumbbell/spherical shape to its graph? Cc @JohnRennie please have a look when you are back

@GaurangTandon I can tell you how to identify these graphs, the way JR taught me.

@Abcd yep, I know, I've read that old chat already, but it didn't help me :(

@GaurangTandon Even before that, in h-bar. Like in July 2017 ...

Which chat did you read?

11:06 AM

@Abcd oh, can you send me that link? I've read the one in PSS instead

@GaurangTandon Which one of PSS?

@GaurangTandon:

in The h Bar, Jul 1 '17 at 6:01, by Abcd

@JohnRennie Just a minute. Let me upload an example picture.

I was reading this chat.stackexchange.com/transcript/54160/2018/3/2 ok will read what you sent

11:31 AM

@GaurangTandon did it help?

@Abcd just finished reading it, yes, it was very insightful! :D I'm trying to digest all of it

Actually I think that resolved my query entirely, thanks @Abcd :)

Q: Why buoyancy is applied on centroid?

12:13 PM

4

My book says: "The point of application of the buoyancy force is the geometric center(centroid) of the submerged part of the body, whereas the specific gravity of the fluid is constant." But why buoyancy is applied on centroid?

buoyancy hydrostatics

What is the energy of the state $s_1$ in units of the hydrogen atom ground state energy?

I wish to ask what does that notation $s_1$ stand for?

$s_1$ ?

I'm not familiar with that notation.

12:32 PM

@JohnRennie please have a look at the solution they have given. postimg.org/gallery/214ikwr6w they might be using a wrong notation to refer to some existing concept

You might be able to recognize that concept

@GaurangTandon I don't really get what's being asked there. The question is straightforward enough. The energy of a one electron atom/ion with a nuclear charge $Z$ is $13.6 Z^2$.

Yes

Then?

@GaurangTandon what is actually being asked? The images you posted don't give the question.

23 mins ago, by Gaurang Tandon

What is the energy of the state $s_1$ in units of the hydrogen atom ground state energy?

This is the question, I sent you the solution in images

Answer is 2.25

It appears to be asking for the energy of the $Li^{2+}$ 2s orbital energy

Which comes out to be 2.25 times the $H^+$ 1s energy

12:46 PM

Yes I understand that

But I have never seen the notation $s_1$ and I don't understand what it means

In the solution, they also referenced $s_2$

@JohnRennie oh, must be wrong then. this is the only time I've seen this notation as well

@JohnRennie I've one more question, are you free?

Yes, I'm around for a few minutes

postimg.org/image/rvf7o1cef/fd9fb370

OK?

12:49 PM

Please have a look at this. I don't understand the last line of the second paragraph ("thus, an electron..." )

Angular momentum must be conserved when an atom emits a photon.

Yes

The photon carries a spin of $1$, meaning it has an angular momentum of erm whatever the formula is, so when the photon leaves the atom the angular momentum of the atom has to change by an equal and opposite amount.

If the electron starts in an $s$ orbital and ends in an $s$ orbital then the angular momentum of the atom hasn't changed, because it was zero to start with and zero after the transition.

@JohnRennie what is "erm"?

erm

Interjection: erm

(Britain) Used in hesitant speech, or to express uncertainty; um, umm.
She was going to, erm... the salon, I think.
(Britain) Used to express embarrassment or subtle disagreement.
Erm, I don't think that was supposed to happen.
- Bob would never say something like that!
- Erm, he just did.

Noun: erm m

arm

Used in hesitant speech, or to express uncertainty - I can't remember the formula for the angular momentum offhand :-)

$\hbar\sqrt{something}$ ?

12:56 PM

Oh ok I thought it was a physical unit :P

Ok please go ahead

Anyhow an $s \to s$ transition emitting a photon wouldn't conserve angular momentum

Yep

And an $s \to d$ wouldn't conserve angular momentum either.

@JohnRennie Question.

It has to be a change of $\ell = \pm 1$ to balance out the change when we create a photon.

@Abcd Yes?

12:59 PM

@JohnRennie question 7^^^

Wrong picture :/

@JohnRennie oh ok I get it. Is it possible though that the angular momentum change due to a single transition of one electron be balanced by emission of more than one photons?

1 min ago, by Abcd

@JohnRennie question 7^^^

@GaurangTandon imgur is better for uploading pictures. Both your pics are rotated as well :/

@GaurangTandon erm (hesitation again :-) I think the probability of multiphoton emission is so small that in practice it never happens. But yes, in principle it could happen so a $s \to d$ transition isn't completely forbidden, just exceedingly unlikely.

@Abcd Wow!

@JohnRennie Why?

@JohnRennie oh alright thanks!

1:03 PM

I guess you have to calculate the force as a function of extension, then show $F \propto -x$ so you get SHM. The constant of proportionality will give you the frequency.

@JohnRennie I was trying to use the energy method (@AvnishKabaj @GaurangTandon please try as well)

@JohnRennie So we get:

$U = kx^2 + mgx+ 1/2 mv^2 $

Isn't it?

And $dU/dt = 0 $

@Abcd oh I didn't realize that :/ sorry, will take some time to get used to these mobile, it's my first day on mobile chat

I'm not sure I would use potential energy to do it. You just need to calculate the tensions in the strings.