Problem Solving Strategies

Kavin Ishwaran

04:30

@JohnRennie Hi !

John Rennie

Hi :-)

Kavin Ishwaran

20 hours ago, by Kavin Ishwaran

@JohnRennie I remember you saying when a light ray is passed through a slit, it wavefunction changes (causing photons to deflect by an angle) so we are seeing interference pattern, But how can a light wave simply deflect because it is passing through a slit ?

John Rennie

Have we talked about Huygen's principle for light? The idea that every point on a wavefront acts a point source of light?

Kavin Ishwaran

Yes

But we haven't talked about how it happens through quantum mechanics

John Rennie

Photons are not like little balls of light. That is, if you look at a light wave with a super microscope you wouldn't see a mass of tiny points of light. You'd just see a wave. This is true in both classical and quantum mechanics.

The photons only appear as point like particles when the light interacts with something e.g. when it interacts with the screen.

Kavin Ishwaran

04:38

Yes

John Rennie

So it isn't appropriate to try and understand diffraction by considering how individual photons travel.

The light wave diffracts at the slit like any other wave diffracts at a slit because it is a wave even in quantum mechanics.

Kavin Ishwaran

Oh !

John Rennie

That is the wave function of the light is diffracting like any wave does.

Kavin Ishwaran

Then ok :-)

John Rennie

We only see a particle when the light interacts with the screen to create a dot of light.

Kavin Ishwaran

04:41

Yes

John Rennie

Even physicists argue a lot about how exactly photons should be interpreted :-)

Wolgwang

@JohnRennie Hi!

John Rennie

Hi :-)

Wolgwang

@JohnRennie Tommorrow is JEEA ! :)

John Rennie

What are you going to do today? Try to relax?

Wolgwang

04:51

Yup. Just some light reading of formulae.

John Rennie

That's what I'd do. You're not going to learn anything useful today, and you want to go into the exam tomorrow well rested and relxed.

Wolgwang

Wish me luck ;-)

John Rennie

Good luck! :-)

Wolgwang

Thanks :)

John Rennie

It's traditional in the UK to say "Break a leg!".

3

Wolgwang

04:55

Don't be happy! I will still pester you after JEE A. XD

John Rennie

:-)
I still chat to students who are at IITs, but they often ask me question that are too hard for me to answer :-)

Kavin Ishwaran

05:06

@JohnRennie Oh :-)

@Wolgwang All the best ! :-)

ronak jain

@Wolgwang Best of Luck For the exam :)

John Rennie

@KavinIshwaran See:

81

A: Do photons truly exist in a physical sense or are they just a useful concept like $i = \sqrt{-1}$?

There is lots of experimental evidence that the electromagnetic field exchanges energy with atoms in discrete chunks, and if we call these chunks photons then photons exist. Which is all very well, but my guess is that you’re really interested to know if the photon exists as a little ball of ligh...

Wolgwang

06:20

@KavinIshwaran Thanks :)

@ronakjain Thanks :)

cOnnectOrTR 12

06:33

@JohnRennie sounds like pressure thing. Things move from higher pressure to lower pressure.

But not vice versa.

Yes @JohnRennie ?

John Rennie

@cOnnectOrTR12 Hi :-)

cOnnectOrTR 12

Hi

John Rennie

Yes, in fact it is just like pressure.

cOnnectOrTR 12

Electrostatic force ?

John Rennie

You can think of the high salt concentrations as having a high pressure and the low salt concentrations as having a low pressure. So salt moves from the higher to the lower pressure regions.

In fact it is called osmotic pressure:

Osmotic pressure

Osmotic pressure is the minimum pressure which needs to be applied to a solution to prevent the inward flow of its pure solvent across a semipermeable membrane. It is also defined as the measure of the tendency of a solution to take in its pure solvent by osmosis. Potential osmotic pressure is the maximum osmotic pressure that could develop in a solution if it were separated from its pure solvent by a semipermeable membrane. Osmosis occurs when two solutions containing different concentrations of solute are separated by a selectively permeable membrane. Solvent molecules pass preferentially through...

Kavin Ishwaran

06:44

@JohnRennie A brief answer that I needed :-)

John Rennie

@KavinIshwaran OK :-)

@cOnnectOrTR12 It's actually caused just by random motion. No forces are involved.

This is true of gases moving in a pressure difference as well.

cOnnectOrTR 12

Gases move from higher pressure region to low pressure region?

I have experience with water. It moves from high pressure region to low pressure region. But salt ?

John Rennie

@cOnnectOrTR12 Yes

Kavin Ishwaran

@JohnRennie Suppose if I have pure water on one side and NaCl solution on other side seperated by a semipermeable membrane, then the pure water will fully mix with NaCl solution right ? (by the formula P = iCRT)

John Rennie

@KavinIshwaran Yes

Kavin Ishwaran

06:55

So there will be no pure water left on the other side

John Rennie

@KavinIshwaran What happens is that as water molecules move into the NaCl solution it increases the pressure in the NaCl side of the membrane, and this inceased pressure pushes the water back.

Kavin Ishwaran

But pressure depends only on the concentration of solute right

Then in pure water C= 0

John Rennie

The system comes to equilibrium when the pressure difference between the two sides balances out the motion of water into the NaCl side.

@KavinIshwaran No, if water is moving to the NaCl side then the number if molecules in the NaCl side increases. If you keep the volume constant that means the pressure increases.

If you allow the NaCl side to expand, and the water side to shrink, so the pressure stays constant then yes all the water will move into the NaCl solution.

Kavin Ishwaran

Oh

@JohnRennie Yes

cOnnectOrTR 12

@JohnRennie I am confused. Only salt molecules move from high region to low concentration region ?

Ajay

07:04

no..

John Rennie

High concentration of salt = low concentration of water, and low concentration of salt = high concentration of water. Yes?

Ajay

Nvm

cOnnectOrTR 12

@JohnRennie in a unit volume?

John Rennie

Suppose on average we have 20% salt. That means there is 80% water. Yes?

cOnnectOrTR 12

Yes

John Rennie

07:07

Now suppose we have a region where there is a higher concentration of salt e.g. 21% salt. If there is 21% salt there must be 79% water. Yes?

cOnnectOrTR 12

Yes

John Rennie

So in this region the salt is increased from 20% to 21%, but the water has decreased from 80% to 79%.

So a region of higher salt concentration is also a region of lower water concentration. Yes?

cOnnectOrTR 12

Yes

John Rennie

So the salt ions are going to flow out of the higher concentration region, but the water molecules are going to flow into this region i.e. the salt and water move in opposite directions.

cOnnectOrTR 12

Ok

And why they move in this way?

John Rennie

07:26

It's because molecules in a solution move randomly in all directions.

Suppose you are at some point in a solution that is 20% everywhere.

cOnnectOrTR 12

Are you saying where the salt concentration is higher there is more pressure due to more random motion of salt molecules and where the water concentration is higher the pressure is low. Water doesn’t have that much random motion. So the result is they move in such way to even out the concentration.

John Rennie

Then there will be some molecules moving randomly past you from the part of the solution on your right side, and some molecules moving randomly past you from the solution on your left side. Yes?

cOnnectOrTR 12

Yes

John Rennie

But suppose the part of the solution to your right has a higher concentration of salt. If there are more salt molecules to you right then more salt molecules per second will move randomly past you than from the lower concentration to your left.
Yes?

cOnnectOrTR 12

Okay

John Rennie

07:39

So that means on average salt will move from the hogher concentration to the lowr concentration region just due to the random motion.

cOnnectOrTR 12

Yes

cOnnectOrTR 12

07:51

So you are saying anywhere in a solution if there is a difference of salt concentration then due to random motion more salt moves to the region of low region compared to salt that moves out of the low concentration region. And that balances the salt everywhere in the solution.

John Rennie

Yes

The same happens with gases. The random motion of gas molecules is how the pressure equalises.

cOnnectOrTR 12

I was in doubt why they will move to a region of low concentration. Why doesn’t every salt molecule move to one part of the solution.

But I guess the salt will move where it will get space.

John Rennie

Yes

cOnnectOrTR 12

Plus if that would happen we would get pure water in one part and highly concentrated salt water in another.

Thank you John :)

Ajay

@JohnRennie Hello :)

John Rennie

08:00

@Ajay Hi :-)

Ajay

For the experiment i'm doing, what should the controlled variables be?

I can only think of the inductor

John Rennie

Yes. If you are varying R and C and the frequency it's only L that you are holding fixed.

Maybe also the voltage of the oscillator, though that shouldn't make a difference anyway.

The room temperature?

Ajay

How would that affect it though?

John Rennie

I'm not sure. That's why I put a question mark at the end :-)

In any case are you controlling the room temperature?

Ajay

No

John Rennie

08:16

So don't include it as a controlled variable!

It's hard to see how the temperature would make any difference anyway

Ajay

Is it possible to do any of these without having done the experiment?

At this point I really don't have much time anymore

Before my first draft is due

John Rennie

Well you can write the method for section 3 and draw the diagrams for section 4.

Ajay

What I was thinking( I know this is academically dishonest, but there have been some tough personal circumstances) Is using the capacitors the school has and making up all the calculations on the sheets. Then using those to do the rest...

Because the experiment will take quite a while won't it

Actually I won't do that

i'll try to do the experiment but if it takes too much time, I will just make up the remaining data

@JohnRennie Why do I need the oscilloscope for the experiment?

John Rennie

08:33

The experiment will take you a single morning. Four hours at the most.

Ajay

Ok :)

i'll give that a try

Ajay

08:50

@JohnRennie But why is the oscilloscope needed?

John Rennie

@Ajay Multimeters are not guaranteed to work at all frequencies. If you're going to use the meter test it first. Conenct it to the signal generator, set the voltage to 1V, then vary the fequency from 20Hz to 20kHz and check the meter shows 1V for every requency.

Ajay

As in, what is it measuring.

Ok

John Rennie

Oscilloscopes are designed to work at all frequencies so it will work everywhere from 20Hz to 20kHz and indeed all frequncies.

@Ajay The oscilloscope is just measuring voltage, but it's guaranteed to work at all frequencies.

Ajay

Ok

Here is a diagram I created

Should I have 7 different diagrams showing the different capacitances?

If not, what symbol (if any) should I use to show that the capacitance is being varied?

John Rennie

Not that's fine. Just state in the notes that the capacitor can be varied.

There is no point in drawing seven diagrams that are exactly the same except for the capacitor.

10kΩ might be a bit high for the resistor ...

I'd start with 1kΩ and see how that works.

You can use the spreadsheet to check.

Ajay

09:04

But R should be kept constant right?

John Rennie

Yes

Ajay

So I need to find the value of R that works best

Can I use the spreadsheet to check?

John Rennie

Yes

Ajay

Ok, let me do that now. I'll update you when i'm done.

John Rennie

The resistor does not affect the frequency of the peak, but it will make the peak wider.

Ajay

09:06

Why would it make the peak wider?

John Rennie

The reason we get the peak is that away from the peak the LC resistance is higher than the resistor, and at the peak the LC resistance is lower than the resistor.

But if you make the resistor too big the LC resistance is still lower than the resistor away from the peak.

This makes the peak smaller. A side effect makes it wider as well.

You can see this in the spreadsheet. You can see the width of the peak widen as you increase the resistance.

Shimura Variety

11:49

@JohnRennie
Good morning sir its been long :smile:

Damn man I didn't study at all for advanced

Transcript for

Problem Solving Strategies