Problem Solving Strategies

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Lllt

04:26

@JohnRennie Hello , are you free sir?

John Rennie

@Lllt Hi :-)

Yes I'm free.

Lllt

Ok sir

Sir when we suppose give positive charge to a conductor it spreads across surface

Now when this charge has uniformly distributed itself, there woill still be mutual repulsion between these charges, yes??

John Rennie

Yes

That's what the "self energy" is.

Lllt

(It will not uniformly distribute if it's random shape, i wrote uniform by mistake )

Yes that's the self energy but what is holding this charge together'

I mean why does charge not flies away

John Rennie

If we have some chunk of metal and we remove electrons from it then that metal will stay positive unless it can attract electrons back onto it from its surroundings.

Lllt

04:35

Ok but what force holds the charge together

John Rennie

But there generally aren't electrons just floating around in the surroundings, so the metal has nowhere to get those electrons from.

Lllt

@JohnRennie Yes , also air is non - conducting

John Rennie

Yes. So the metal stays charged because there is no way for charge to flow onto or off of it.

Lllt

Yes I get that but is there some unknown force which holds them together

John Rennie

If we consider an uncharged piece of metal then the metal atoms are held together because they form chemical bonds with each other. That's what gives metal its strength. Yes?

Lllt

04:38

Yes metallic bonds

John Rennie

Now we can give the metal a positive charge by pulling electrons off it, but the number of electrons we can pull off is a tiny fraction of the number of electrons in the metal. So charging the metal makes essentially no difference to the strength of the bonds holding the metal together.

Lllt

Ok so it is still those chemical bonds holding the positive ions and electrons together

John Rennie

Yes

Lllt

Thankyou sir it's clear :-)

John Rennie

:-)

1 hour later…

Adil Mohammed

05:45

@Lllt Next year i guess, though i may take a gap year also to chill

Lllt

06:41

@AdilMohammed JEE 2022 you mean?

Robin Singh

07:01

@JohnRennie Hello sir :-) how are u doing?

John Rennie

@RobinSingh Hi :-)

I'm good, how are you? Is your college reopening soon?

Robin Singh

I am fine sir. No sir actually i am yet to give jee so...

i had a doubt from inductors. Are u free?

John Rennie

Ah, for some reason I thought you were already at college. Oh well. Yes, post the question and I'll have a look.

Robin Singh

Suppose switch is in 1 for a very long time and now it is turned to 2. Now, current in A will be some i and in B it is 0. But how is that possible? They are in series so they should have the same current, no?

John Rennie

Yes, when the switch is in position 1 the current in B is zero, but when the switch is in position 2 the currents in B and A are the same.

Robin Singh

07:12

But an inductor doesn't allow a sudden change of current in itself, no?

John Rennie

Hmm

We have two opposing effects. The current in A doesn't want to stop suddenly, and the current in B doesn't want to start suddenly.

In principle for ideal inductors and an ideal switch this would cause an infinite potential across both inductors.

In practice we don't have to worry about exactly what happens when we close the switch. All we need worry about is that the energy in the inductors is conserved when we close the switch, and after closing the switch that energy is shared between the two inductors.

Robin Singh

Ah alright sir. I think I can do the actual question now

John Rennie

OK :-)

Lllt

@RobinSingh All the best for your exam :-)

Robin Singh

07:39

@Lllt Thanks bro! I think u told me but are u 2021 too?

Lllt

07:57

@RobinSingh No I am preparing for next year .

Robin Singh

@Lllt cool, hope u r going good

Lllt

@RobinSingh Yes I started late and have some backlog but I will clear it

2 hours later…

Robin Singh

10:12

@Lllt ah yes u will get plenty of time to clear backlogs after ur syllabus is finished. Even I didn't attend a coaching in 11th so had a lot of backlog but now it's all good. But I'll have to give half of the credit to corona for delaying jee

1 hour later…

Samyak Marathe

11:25

Greetings

I have a question to ask, if anyone is free.

@JohnRennie

John Rennie

Hi :-)

Samyak Marathe

If you are not busy I have a question

John Rennie

Yes ... ?

Samyak Marathe

So the question is: If Magnetic field due to a long wire is 0.4Tesla at a distance r. If the distance is doubled, what is the field

Now wait for an image

John Rennie

Do you know the equation for the magnetic field due to a current I in an infinite wire?

Samyak Marathe

11:30

yes

but the answer through my approach is coming 0.1 Tesla, though I m familiar with the formula for infinite wire

John Rennie

B = μ₀I/2πR
Yes?

Samyak Marathe

just a min.

I m typing about the question

${\huge B} = \frac{\huge\mu_oi}{\huge2\pi R}$

by that the answer is 0.2 Tesla right?

John Rennie

Yes

Samyak Marathe

But I did as follows:

${\huge 0.4} = \frac{\huge\mu_o}{\huge4\pi } {\huge \int} \frac {\huge dl \sin\theta}{\huge R^2} $

${\huge 0.4} = \frac{\huge\mu_o}{\huge4\pi } {\huge \int} \frac {\huge dl \sin\theta}{\huge (2R)^2} $

when distance is doubled

which on simplification gives:

sorry

John Rennie

So you're using the Biot Savart law?

Samyak Marathe

11:40

${\huge B} = \frac{\huge\mu_o}{\huge 16\pi } {\huge \int} \frac {\huge dl \sin\theta}{\huge R^2} $

on simplification it gives this

yes biot-savarts law

now I divide both the equations

and the integration part gets canceled

now I divide

btw I missed I in both equations

${\huge \frac {0.4}{B}} = \huge (\frac{\huge \mu_o i}{\huge 4\pi } {\huge \int} \frac {\huge dl \sin\theta}{\huge R^2} \huge) / \frac{\huge \mu_o i}{\huge 16\pi } {\huge \int} \frac {\huge dl \sin\theta}{\huge R^2}$

${\huge \frac {0.4}{B}} = \huge4$ $or~ \huge B = 0.1T$

is it correct?

because if the angle is almost 90 for infinite wire, in that case the integration part should get cancelled

John Rennie

I'm not convinced your integral is correct ...

But I have to go now, so we'll have to look at this later.

Samyak Marathe

but if this is wrong, why is that correct

1 hour later…

satan 29

12:58

@SamyakMarathe the distance "r^2" in biot-savart's law is the distance of the dl elements from the point in question

so if you take an element "dl" at a length l along the wire, and your point is at a distance 2R from the Midpoint of the wire, then the "r^2" in BS law is l^2 + (2r)^2

RaMathuzen

I have a doubt about this Irodov question that is many solution providers in net use $P{0} \cdot l = P \cdot (l-x)$ but we can only use $P{0} \cdot (l-h)$ where h is the height of capillary rise(initially)

Samyak Marathe

13:54

@satan29 I didnt understand

Q: Find the magnetic field of an infinite wire at distance $2R$, given the field at distance $R$

If the magnetic field of an infinite wire at a distance $R$ is is $0.4 \;\text{T}$, find the field at a distance $2R$. The approach suggested by internet is as follows: Magnetic field due to an infinite wire is: $$B = \frac{\mu_0I}{2\pi R}$$ or as given: $$0.4 = \frac{\mu_oI}{2\pi R}$$ When R i...