Problem Solving Strategies

« first day (1697 days earlier) ← previous day next day → last day (926 days later) »

4:21 AM

@YashAgrawal lorentz force is frame independent, so when you move with v along with the charge, the force is according to the lorentz force which is the same as an electric field having magnitude v x B

Yash Agrawal

@napstablook but there is no electric field

neither any magnetic flux is changing by which we could say that electric field is induced

@JohnRennie sir can you have a look into it

John Rennie

4:42 AM

@YashAgrawal Hi :-)

I'm busy with another question at the moment but I'll look at this as soon as I'm free.

Yash Agrawal

@JohnRennie Sure sir , look whenever you are free , no hurry

1 hour later…

John Rennie

5:55 AM

@YashAgrawal This is in some ways complicated and in other ways surprisingly simple. It's because when you move relative to a magnetic field then to you that field looks like a combination of magnetic anD Electric fields.

Likewise if you move relative to an electric field it looks like a combination of electric and magnetic fields.

satan 29

6:11 AM

@YashAgrawal en.wikipedia.org/wiki/…

however your question suggests that the E field for the observer should be VxB...however as per the wiki it should be $\gamma v \times B$..

hmm whats the argument for the gamma..

John Rennie

@YashAgrawal This is the result of special relativity. You've probably heard that in SR we get weird effects like time dilation and length contraction. Well another effect is that electric fields turn into magnetic fields and vice versa.

Yash Agrawal

@JohnRennie But can't it be understood from maxwell equations alone ?

John Rennie

@YashAgrawal Yes it can, and that's because Maxwell's equations are actually special relativistic equations.

Indeed Einstein developed relativity starting from Maxwell's equations.

Maxwell didn't realise it at the time, but in a sense he discovered special relativity!

Yash Agrawal

Actually So how can we predict that electric field is induced in my moving frame by maxwell equations ?

not by effects such as length contraction and time dilation

satan 29

I dont think "induced" is the right word...or is it?

John Rennie

6:29 AM

@YashAgrawal You need to use an equation called a Lorentz transformation.

I must admit I have forgotten the details though i don't think it's that complicated.

satan 29

its in the Wiki link

John Rennie

Q: Lorentz transformation for electric and magnetic fields

How do derive the following transformation rule (J.D. Jackson third Edition 11.10) for electric and magnetic field? $$\vec E' = \gamma \left( \vec E + \vec \beta \times \vec B\right) - \frac{\gamma^2}{\gamma +1} \vec \beta \left( \vec\beta \cdot \vec E \right ) \tag{1}$$ $$\vec B' = \gamma \left(...

Yash Agrawal

sadly I'm unaware about it ;/

John Rennie

You won't cover this stuff unless you do a physics degree, and even then probably not until the second year of a physics degree.

That need not stop you learning about it for fun, but you do need to know a bit about special relativity.

satan 29

@JohnRennie whats your explanation for the extra gamma?

according to that question, the E f in the observer frame should be vXB

but according to lorentz it should be $\gamma v \times B$

John Rennie

6:34 AM

I can't remember the derivation. It's decades (literally) since I last studied this :-)

satan 29

hmm but seems a bit odd

Yash Agrawal

so lorentz transformations are direct consequences of special relativity ?

John Rennie

@YashAgrawal Yes

Wolgwang

> A cart of mass M moves at a speed u on a frictionless surface. At regular intervals of length L, blocks of mass m = M/2 drops vertically into the cart. How much time is taken to cover a distance of 9/2 L?

So according to the question, the cart is moving on the ground and blocks are dropping from the sky?

Yash Agrawal

@JohnRennie but it's not maxwell equation right ?

John Rennie

6:39 AM

@Wolgwang The idea of the question is you are adding a stationary (horizontal velocity = 0) mass to the cart. Since momentum is conserved this means the cart has to slow down.

@YashAgrawal The underlying principle is a symmetry called Lorentz covariance and special relativity is the theory that describes this symmetry. Maxwell's equations obey this symmetry so I guess really we'd say Maxwell's equations are derived from SR.

An the Lorentz transformations are derived from SR.

So I probably wouldn't say the Lorentz transformations are derived from Maxwell's equations or vice verse. Both are derived from SR.

Yash Agrawal

@JohnRennie Ok , I think I understood what being said

Thanks :) , though I will try to get some hand on special relativity if time permits

John Rennie

It's a fascinating subject, but don't let it detract from the JEE prep!

Yash Agrawal

@JohnRennie Yes , I don't think it would be of any use for JEE

satan 29

wait though..that question gets messy I guess

the original scenario will have the charge accelerating .. (theres a Force!) and if we transform to a frame in which there will be zero rel velocity (and hence zero B force), we ll need to accelerate too and this is no longer an inertial frame

Yash Agrawal

6:57 AM

@satan29 I don't see why we need to accelerate , if frame acceleration is zero and velocity is same as charge then relative velocity is still zero

satan 29

but the velocity of the charge is continously changing.

Yash Agrawal

i'm talking about an instant

at a particular instant we are making all the observations

Wolgwang

7:11 AM

@JohnRennie Is there a short trick?

> A cart traveling at speed v on a frictionless track starts to leak sand. What is the cart’s speed at a later time?

Greater than v?

satan 29

7:29 AM

suppose you have the cart + sand as your system.

at one instant, it has total mass M and speed v

it leaks some amount of sand dm, and suppose the speed comes v+dv

momentum conservation in x direction is mv= (m-dm)(v+dv) + dm(0)

which will give you dv/v= dm/m

dm is a positive quantity because i have arealdy assumed the - sign in the mass being (m-dm), so dv is a positive quantitu, i.e the velocity is increasing

which is common sense with that mom. consv. argument but you can now evaluate stuff numerically

as an example, suppose sand leaks at a constant rate $k$

and k is positive

then $dm= k dt$ and $m= m_{0}- kt$. so

$\int_{0}^{t} dv/v= \int_{0}^{t} kdt/m_{0}-kt$

$v(t)= v_{0} m_{0}/ m_{0}-kt$

I defined the quantity $dm$ a bit awkwardly : it is the amount of sand leaked out. normally dm would mean the change of in the mass of the system, in which it would be a negative quantiity and you would write the mass of the whole thing as (m+dm). But anyways, in the end youll get something like this only: v= v0*m0/m(t)

2 hours later…

RishiNandha Vanchi

10:18 AM

Hey guys

Anyone joinin IITM?

cause we might meet 👀

@JohnRennie All my friends did better in mains than advanced Sir XD

I think its because half the mains chemistry questions are not even testing anything but mugging up that ncert book

@Anusha Congrats!

2 hours later…

Anusha

11:57 AM

@RishiNandhaVanchi which branch?

2 hours later…

BannedUser

2:17 PM

I again got one stupid question

why is max friction not u+N and instead u*N?

u is how rough the surface is and N is normal force applied by surface

if you can explain please ping me

my guess is people just like multiplying in physics

Yash Agrawal

2:43 PM

@BannedUser It's just experimental , We have found in reality that maximum friction is proportional to Normal ,where that proportionality constant is termed as u , I guess it's not people it's nature which like multiplying :)

BannedUser

3:03 PM

Ah if I just add a constant then it is meaningless

force+constant

in terms of dimensional analysis

Yash Agrawal

3:13 PM

constant should have dimensions of force to make it work out

1 hour later…

Wolgwang

4:24 PM

> A point object $O$ is placed on the principal axis of a convex lens of focal length $20 \mathrm{~cm}$ at a distance of $40 \mathrm{~cm}$ to the left of it. The diameter of the lens is $10 \mathrm{~cm}$. If the eye is placed $60 \mathrm{~cm}$ to the right of the lens at a distance $h$ below the principal axis, then the maximum value of $h$ to see the image will be

Why do points A,C,D have to be collinear?

Yash Agrawal

5:13 PM

@Wolgwang eye must lie under field of view of image

if eye is below that maximum height it will be able to see the object

though I guess there is a slight problem with the question , as the lens formulae is only valid for paraxial rays and these rays doesn't seems paraxial

6 hours later…

hansika

10:53 PM

https://imgur.com/a/cUsG89e
The question asks "frequency at the instant", at that particular instant it would have received a frequency which train S1 would have emitted at time (say t) ago, and in this time t the train would have covered a distance 30t and would have reached at the the particular instant which question is talking about, so technically shouldn't we have been applying doppler's effect for train S1 t seconds ago?

@JohnRennie Sir, it would be great if you have a look at this question whenever you get time :)

« first day (1697 days earlier) ← previous day next day → last day (926 days later) »

all rooms