If you suffer from aversion towards physics,don't read on.If you don't believe in mathematical/logical treatment of physics,punch the screen.If you are a die-hard fan of H.C.Verma or D.C.Pandey,strangle yourself to death.And if you think your college life(+1 and +2) got wasted because of physics,unbookmark my blog.I don't think you'll like what I'm about to write.(Ah!Wait..You might like some of the conversations between the authors and Anirudh.So go Ahead!)
The concept of purchasing multiple books for a course doesn't appeal to my senses;Instead,I believe in grabbing one book that would give me all that's required.I believe in books that leave a trail leading to discovery/invention.Like any other IIT-JEE aspirant,I bought three books for physics:H.C.Verma(The guy who thought people were dumb enough to accept his statements without proof),Halliday&Resnick(The low-price edition,sold only in India,China,SriLanka,Burma etc., A fat book with a plethora of unnecessary pictures),Irodov(All Hail to the master).Ooops! How did I forget to mention cheap-ass D.C.Pandey ,who did nothing more than Ctrl-C + Ctrl-V + a few changes(only reason for a litany of errors) of the above stated books.By now you might have realized that I consider D.C.Pandey's books as inferior.In fact,you can call them as
When it came to physics in +2,I was an average student...
When I repeated for IIT-JEE, Prof.L.N.Prushti dragged me out of the dungeon of ignorance.
Driving force for the following section:His lectures,coupled with Irodov's books and long discussions with my friend Navneeth(Now,BITS-Hyd doing EE).
Proof of Coulomb's Law from Gauss Law:
Whenever Indian Authors try their hand at writing/deriving something original,something they are NOT used to,they end up committing huge mistakes..One such flaw is the proof of Coulomb's from Gauss Law.
where L.H.S stands for Electric Flux through a closed surface 'S' and R.H.S is Total charge enclosed by surface 'S' divided by vacuum permittivity.
1.H.C.Verma emphasizes too much on the fact that 'E' in the eq. is the net electric field,but misses out on the validity of the equation across reference frames.Gauss law is valid in ALL reference frames,except ROTATING Frames.
2.The way books derive it is farcical.They start off by saying,"Consider a Gaussian sphere of radius r around the point charge.Now,they say Since 'E' is normal to the sphere,implying that it's parallel/anti-parallel to Area Vector,the L.H.S of Gauss law is equal to E.integral(A) over the surface 'S'.Integral(A) is 4*pi*R^2.Hence we get Coulomb's Law from Gauss law..Everybody is happy because they feel they proved something very fundamental.
Where is the FLAW??
Ans: First of all who told him that 'E' is normal to the Gaussian sphere?? Where is the argument justifying it? They say because field created by a point charge is radially outward(inward depending on the nature of charge),'E' at that point is normal to the surface..Now this is ridiculous..This is a conclusion of Coulomb's law and we CANNOT use it to prove Coulomb's law itself.Gauss law is silent about the direction of field generated by a point charge.
We have to argue to prove our point.It goes like this...Let's ask D.C.Pandey a few questions.You can also choose H.C.Verma.He also committed the same mistake.You will WIN irrespective of the opponent.
D.C.Pandey:Okay,tell me how would you justify that it is radially outward?
Anirudh:Assume,it's NOT normal for a moment.Which direction would you assign???
D.C.Pandey:(Hope he doesn't say I don't know):How about a random direction??Say,One that points to Arihant book house at Meerut!
Anirudh:If you say that,I'll say it points to my home at Hyderabad.You can't prefer one direction to the other,DUDE!
D.C.Pandey: WTF?? Ummm..How about tangential?(With an air of impudence)
Anirudh:Which Tangent?-There are two directions to that vector. If you choose one,I'll ask you why not the other!
So,basically I WIN!! BIATCH! Hence the direction is radially outward(normal to the surface)
D.C.Pandey:Thanks for educating me!
Anirudh:Ah! it's alright..And Please DON'T thank me.Thank my prof.When I mentioned your book's name,he passed censorious comments..So,Fuck That..
The rest of the proof is the same.The crucial step: how's E' is normal to the surface.Some authors call it spatial/radial symmetry.Just because someone wrote it as symmetry everybody starts using the same words without knowing it's actual meaning.
Similar argument may be applied for other uniformly distributed charge configurations.Please DON'T apply it blindly-It might lead to erroneous results.
Discontinuity in an electric field:
CLICK TO GET A MAGNIFIED VIEW
Anirudh:As you can see,the above figure indicates the discontinuity in the electric field value on the surface of a uniformly distributed thin spherical shell.
For r less than R,E=0.Otherwise a finite value..
Hence for 'r' tending to R- , E=0 and for r tending to R+,it's a finite value.Therefore,the field experiences a jump discontinuity at 'R'.
H.C.Verma:So what??What's your problem,Anirudh??
Anirudh:What is the value of the electric field at r=R?
H.C.Verma:Lol! I seriously don't know! Wait Let me check my book
He flips through the pages of "Concepts" of physics Vol-2....
H.C.Verma:Sorry! I don't think field exists on the surface of the spherical shell..
H.C.Verma:I didn't write 'bout it in my book.So,it shouldn't be there.I copied from one of the Authors in US.He didn't mention it..So,ditch that!
Anirudh:(I stifled a laughter):F*** the Americans..Do you know IRODOV? Have you ever heard of Russians-Their contributions to the field of physics??Did you know that a 12th grader in Russia knows as much physics as you do?
Okay,lemme educate you on discontinuity of fields:
Theorem:Suppose 'B' is a body with uniform charge distribution.Suppose also that the surface charge density(sigma) is NON-ZERO and FINITE.Then,
a)There is a "jump" discontinuity in the field value on the surface.
b)If the field vector is resolved into two parts(normal and tangential),then only normal component suffers a discontinuity.The tangential component is always continuous.
c)The normal component of the field on the surface is given by the "Arithmetic mean" of the field Vectors" in the neighborhood of that surface.
d)The difference in the normal components of the field is chargedensity/permittivity.
You can refer BASIC LAWS of Electromagnetism by I.E.IRODOV for the proof or CALL ME or SkypeME(anirudh.s2005) for further details about the proof..
An imitation of Irodov's proof:http://physweb.bgu.ac.il/COURSES/Electro1/extra/Discontinuity_in_an_Electric_Field.pdf
H.C.Verma:So,you mean field value on the surface is half the field value just outside the surface!
Anirudh:Wow!! At least you figured this one..
H.C.Verma:Not just that..I also understood why the field on the surface of a uniformly charged disk is ZERO..
H.C.Verma:Hey,don't leave..According to your theorem there must be a discontinuity in the field value on the surface of a uniformly charged sphere with volume density "Rho"?
Anirudh:Huh?? I thought you made conceptual errors..Now,I understand that you have a problem reading the hypothesis..
For people like you,I highlighted words like FINITE and NON-ZERO...
Since sigma=rho*thickness and thickness tends to zero in a uniformly charged sphere-sigma=0.
Hence there is NO discontinuity!!
D.C.Pandey:WTF???What do you mean by discontinuity in fields???? Discontinuity is a concept in maths,NOT in physics!
Anirudh:Can anyone lend me a gun??
Oppositely charged point-charges moving towards each other:
This problem was copied from IRODOV's book..And without shame the authors solved it from ground frame(K-frame).The problem is to evaluate the velocity of each point charge when the distance becomes half the initial separation..
It's not wrong to solve the problem from the ground frame.You have to justify it..
Dude,it's electrostatics:We deal only with charges at rest.Only when a charge is at rest the field is CONSERVATIVE ,a POTENTIAL function exists..
From the Ground-Frame,both the charges are moving and hence they aren't static anymore...
So the force between them is NOT given by Coulomb's law-It's something else...
Hence Potential energy is NOT defined for this system from GROUND frame..
Luckily,the answer turns out to be the same whether you solve it from the ground frame or the frame of reference of one of the charges because work done by internal forces is independent of the frame of reference...
Also one must justify this by going onto the reference frame of one of the charges.When I'm on one of the charges,the field is Electrostatic and hence Conservative..
Now,at this stage one must switch from charge frame to ground frame and Solve the problem..
For more info,you can SkypeME(anirudh.s2005) or MailMe(email@example.com)
D.C.Pandey:I have an intelligent doubt..Can Potential function suffer discontinuity??
You are a disaster..Why did Arihant publishers give you a Santro Car? You don't know what Discontinuity is and now you blabber as if you know everything about it..
Okay..Here's an assignment for you,Pandey:Prove the following theorem..
Theorem:Potential Function is always continuous...
I came to know you like the problem of parallel plates ..My friends told me your book has a huge set where you earth plates to the ground and ask them to calculate the charge on each plate..Here's a small question.
Q)i)Find what's the charge on the extreme surfaces?
ii)If you guessed a particular value(I know you would have guessed it as zero),Prove why it is zero!
Take your own time..Submit the assignment before you die..
Capacitors with Dielectric:
One of the example problems of H.C.Verma is a duplicate of Irodov's problem.See pg no.163 (Concepts of physics vol-2)..The problem was to find the rise in the level of liquid dielectric in the capacitor when a charge is imparted..
The answer to this problem is wrong because the model of polarization is an outdated one where charge is considered only at the boundaries..There is charge in the bulk too.Who will find the force of that?? Tera Baap kya?
Here is another Ridiculous problem:
There is a capacitor with a dielectric.The dielectric is connected to a pulley which has a mass 'M'.The weight of the 'M' pulls the Dielectric down and the dielectric executes Simple harmonic motion..Find the TIME period of S.H.M...
This problem is correct only till executes S.H.M..After that,it's bogus..
There are many aspects to this problem
a)Why does it exhibit S.H.M or say an oscillatory motion?
(Hint:To answer this you have to find out whether there is field outside the capacitor..Answer is:Yes..there is a fringing field and it is non-uniform(PROVE THIS FIRST)..We have to use the "del" form of force to prove that there exists an inward force..
After that,it's impossible to proceed further as the capacitor is connected to a battery;As the dielectric moves,the battery removes charge from one plate and places it on the other..So the charge on the plates of the capacitor is
changing w.r.t time..The charge is not static implies field is not static and hence NON-CONSERVATIVE force..So one cannot solve this problem in Electrostatics..
D.C.Pandey went one step further and asked the readers to find the VELOCITY OF THE DIELECTRIC..FTW???
*****End of Vol-I******
*****End of Vol-I******
Any new thoughts/proofs/contradictions to my views can be posted as comments..
(Charge is invariant.Thus,content related to it ought to be invariant)