The wrong questions and responses in GATE 2018, Physics. Reply

Here is a summary of the questions which has possibly been set wrong (I have given details below) or numerical answer types whose answers have been given incorrectly as per the declared answer sheet.

Q8. The magnetic field also has a odd parity. Not “E and A only”. Since that choice (or “none of the above”) isn’t given, clearly the question has been set wrong. See here.

IMG_20180220_193219_2

Q3. The Stern-Gerlach experiment evidenced space quantification of angular momentum. The Zeeman effect evidenced the existence of electron spin. That choice isn’t given, instead answer sheet gives the opposite as the correct answer. See any good text on quantum mechanics. eg “Quantum Mechanics 2nd edition, Bransden, Joachain” page: 37 and 38. To avoid any ambiguity, Its the S-G experiment which evidences space quantization (of both spin and orbital angular momentum). But Zeeman effect evidences electron spin only. It was the anomalous Zeeman effect which had led to the discovery of electron spin.

zeeman

There are also two NAT type questions which seems to be way off in the correct responses as per the exam conducting body. But the calculations shows somebody missed something somewhere. They are questions 48 and 49 according to the uploaded answer sheet and question paper. I have performed the detailed calculations in this pdf file:  gatephysics_2018.

Altogether this is 6 marks and 2/3 marks for the Q3 and Q8 if they have been deducted wrongly. So, 6+2/3 marks. I haven’t been able to find any more lapses although it was very tempting to feel so.

Wrong question in GATE 2018 physics? 1

Gate Physics 2018: Parity of vectors.

I think the above question asked in GATE 2018 (physics) is wrong.

Any vector has two components. The component perpendicular to the parity axis has even parity and the parallel component to the axis has odd parity.

The opposite is true for axial vectors.

E, A vectors.
B, L axial vectors.

The correct answer per gate exam body is E, A. Why not B and L? It’s an arbitrary situation and perpendicular components of these fields will have odd parity.

So the question since it does not specify the direction might be wrong. Unless I’m missing anything. What’s your idea ?

I am adding one relevant page for why the answer might be wrong. (A question is wrong, when all possible answers given are, wrong. That seems to be the case here.) For detailed answer and any other relevant page, check here. [Prof. S. Errede’s handouts. UIUC]

According to this lecture note from a famous university (UIUC) among E, B, L and A except L all others have odd parity. L doesn’t as its made from cross product of two vectors (r and p) which both have odd parity. There are several ways to see why B has odd parity as well. One is to see it as B = curl A. A has odd parity and grad operator has even parity. Check page 5 of the linked note from UIUC.

 

So except L all others have odd parity. [E, B and A]. Putting the phrase “only” makes the question erroneous. Because e and A pair is right but its not the only ones among the given vectors which has odd parity.

parity

 

Scilab for classical dynamics course. 1

Yesterday I had uploaded a list of practicals that can be done using scilab for a nuclear and particle physics course I was teaching last semester. Here is a list for the classical dynamics course which I wasn’t teaching but asked to engender a scilab course for. Its small compared to the nuclear physics list but nonetheless can be augmented in a similar spirit per your choice.  The following versions are slightly updated from earlier uploaded versions. PDF ClassicalDynamics_scilab DOC ClassicalDynamics_scilab

 

If you are to come out of a NET that traps you. Stratagem. Reply

If you are to come out of a NET that traps you. Stratagem.

This article is purported to be helpful towards those who take Indian after the university entrance exam known as NET (National Eligibility test governed by CSIR; Council of Scientific and Industrial Research) twice every year. [Science NET is known as CSIR-NET and arts/humanities as UGC-NET.]

Manmohan sir, I want to qualify net. … any suggestions ?

I am assuming you will take the test in June 2018.

Solve 10 previous papers thoroughly.

Make a categorization of subject wise weightage: eg mathematical physics, quantum mechanics, thermodynamics etc.

Set yourself a good score based on what you think you can certainly achieve. Make a 15% increase and make that your target.

See your strongest subjects and make a plan which ones you want to be thoroughly prepared about so you can arrive your target.

Never attempt a question, unless you are very sure of it. Negative marks in net can ruin your chances. (By attempt I mean: select the choice)

Decide in which section you want to score how much.

In section A (total marks 30) try to achieve full marks, except a few daunting questions. Getting 22 (11 questions right, assuming no negative score) seems a good idea. In section B (20 questions in total) try as many as you would like, to comply with your target. eg if your target is 110/200 you already got 22. So lets say you think you can score 35 in sec B (10 questions right, no negative) then you have 57 by now. So rest 53 must come from sec C, which is about 11 questions right, without negative scoring. You can vary between sec B and C to fulfill a particular target.

You should take mock tests frequently. Take a previous year question paper, set yourself 3 exam like hours without disturbance and attempt the paper. Now analyse your responses, based on the answer sheet. This way you can gauge yourself properly.

Once you have solved 5 sets of question papers, you know exactly what to be expected in the exam. eg exactly what kind of quantum mechanics questions and so on.

Brush up your concepts thoroughly based on this, from good quality texts. I will give you selection of text books, in the end. Also try to solve good number of questions from these texts. When studying the text focus on the text, not necessarily on exam. So test your understanding based on chapter-end questions. Solve them yourself. If you can’t try to find if solution manual is available. Some texts have answers available, full solutions that is.

Do proper time management, eg skip difficult or lengthy answer type questions for 2nd round. First attempt what you can solve quickly. Here by attempt I mean actually solving the question and not just selecting any choice. Also attempt first, questions, where you are thoroughly prepared. Then go to what you think you can do but requires long amount of time. Then go to attempt what you might think you may not solve but give a shot. Now review your answers for any possible mistakes.

When using scribble pad make each question have a separate space, so you can easily review later, you can leave some space to each questions space, so you can add some calculations during review.

Now go onto solve more and more questions from good study materials. Not necessarily coaching materials. It could be Schaum’s series or a good text book. Keep on taking mock tests to gauge your preparedness and requirements.

Here are some text books to follow, they are my favorite and most of them are quite helpful from NET prospective as well.

A. Mathematical Physics: 1. Mary L. Boas. 2. Riley Hobson.

B. Classical Mechanics: 1. Takwale Puranik, 2. Rana, Joag. 3. Mathur 4. Gupta (the latter two include properties of matter and wave etc)

C. Modern Physics: 1. (one stop) Arthur Beiser. 2. Eisberg and Resnick (book name: quantum mechanics of atoms molecules etc)

D. Electromagnetic Theory 1. Hecht (optics book) 2. Griffith (Ed book) 3. Berkley series (author: Purcell) 4. Mahajan Choudhury (Ed text)

E. Solid State Physics 1. Ali Omar 2. Kittel 3. Beiser (mod physics text)

F. Nuclear Physics 1. Kenneth S. Krane 2. Cohen 3. Prasad 4. Gupta

G. Electronics, Digital electronics 1. author Malvino, Leach, Saha 2. RS Sedha (S. Chand) Analog electronics; 1. VK Mehta 2. Malvino Bates 3 Tayal and Tyagi

H. Quantum Mechanics: Griffith 2. Levi (applied quantum mechanics) 3. Joachain (Pearson)

I. Statistical Mechanics 1. Reif (Berkley physics course, A must for everyone) 2. Pathria Beale (Advanced level, but thoroughly descriptive)

J. Thermodynamics 1. Garg Bansal 2. Zeemansky Dittman 3. University physics (Sears, Zeemansky et al)

You can see/refer difficult texts like Arfken, Jackson or Goldstein on a need basis.

Relativity; follow that thin book Resnick and Arthur Beiser would also help.

I hope that helps.

Cross and Dot product of vectors. 1

Someone asked a very interesting question on role of vectors in Physics. He was curious to know if dot product of vectors is natural but vector product is just syncretism. (that is make shift or unnatural manipulation)
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Every vector can be resolved into two components. The cosine and sine components (any two vectors would constitute a plane) while cos part can represent the projection defined through dot PDT we can’t leave out the sine part. It plays its role through the vector or cross PDT. The vector direction is no more along same direction as original vectors because of orthogonality. To preserve symmetry of both orthogonal components (or equal footing of both vectors, vector a and b eg) we need the 3rd dimension. Hence such a definition of cross PDT. Eg the emf generated in a changing “mag field” (Faraday’s law) depends on change in mag field if area is held const. It also depends on change in “area vector” if mag field is held const. So there are two vectors involved and their transverse values matter (and not their longitudinal values). To preserve equivalent role of both area and mag field vectors the resultant vector must be in a 3rd orthogonal direction …

Also think of this; a scalar is not necessarily directionless. (think electric current or even temperature or heat gradient etc) They just do not have the full fledged capacity of vectors. Its like flower bud vs fully blossomed flower.

SO scalars can’t be added like vectors. We tend to make a mistake here. We say scalars don’t have a direction. That’s totally erroneous. They do have direction and it matters. Which direction you want to stick to if the current flows along certain direction only? Lets make it still more clear. If there are two directions in which there are electric currents, we say they are both equal, the direction won’t matter. That’s where we make the mistake. We should say they are equivalent and not equal. Equality is ideal, its mathematical. But equivalence is physical. Its the effects of both currents in a certain sense that make them equivalent, but their strict equality does not follow.
Talking about equivalence: what matrices are in ideal or mathematical situations, tensors are in physical situations. Just like vectors were row or column matrices in their ideal formulation.
So when forming dot product either of the vectors can lend its direction and the projection of the other vector is multiplied with magnitude of the reference one. Although scalars then become directionless because they are just magnitude of two vectors multiplied together, they still have an innate sense of direction, based on the reference vector. They no more remain as valiant as before when the original vectors were considered. But A.B can be found either along A or B, giving equivalent but not strictly equal result.
But projection is just the cosine component of one of the vector along the other. This discards the other (i.e. sine) component because in the physical nature of things it wouldn’t matter.
If you apply a force perpendicular to some object all it will do is change the original direction of motion, transverse to the direction of force. But it will not change all possible inertia, that is the speed of the motion. As a result it does no work, since the displacement is zero, given the speed did not change. (Force did not produce additional displacement) Magnetic forces are notorious for that. They are lazy. They do no work. They only take you round and round telling you stories, like the HRD ministry. (Frictional forces are the opposite in a sense, they spoil your work, like religious groups.)
So when two vectors are as important as they can collude to act along or opposite to each other, eg displacement and force vector, all it matters, is to know or employ their longitudinal components.
Such components of forces correspond to change of inertia of speed and not direction. In general inertia is just velocity vector, change velocity the inertia changes, as does the momentum, hence the force, that’s the essence of Newtons first and second law. That it changes is Newtons first law and how much it changes second law.
What would happen if a charge which is moving  is placed in a magnetic field?
It would experience a magnetic force. Such forces arise from the effect of two vectors. One; the velocity vector of the charge. Two; the magnetic field vector. And if the velocity is along the field direction, it is seen that the inertia does not change atall. Thus while we expected some amount of work we don’t get any work done, because now there is no force. The only other possibility that remains is when the charge is moving in a transverse direction to the field. All general cases are superposition of both independent or orthogonal cases, the longitudinal or along the line and the transverse or perpendicular to the line, cases. So we need be concerned only, about what happens for the transverse case.
In this case the force depends on two vectors. 1. a. The magnitude of field and b. its direction. 2. a. The magnitude of velocity and b. velocity or motion direction.
The resulting force does not discriminate between the field vector or the velocity vector. And we already saw that there is no force when these two vectors are along a line or opposite to it. We are concerned only about knowing what happens when the velocity vector and field vector are perpendicular or transverse to each other. Equivalence of two vectors would lead to a symmetry. Their magnitude as well as their directions matter equally well. The total effect (like in the case of dot product and work done) is a product of magnitude of two vectors, one with the perpendicular component of the other with respect to the first one as a reference. Thus this satisfies the symmetric situation in terms of magnitude. (i.e. it does not matter which vector you take as the reference, there is only one angle between them, both vectors as reference will give equivalent results)
The only other symmetry that is required is that of direction. The only possible direction which is not biased wrt one of the vectors is “orthogonal to both vectors direction”.
Right Handed or left handed is merely convention left as an anthropic liberty which must be used consistently. Cross product is much more involved than dot product but rightly so. Its not an artificially inseminated idea, just to satisfy our quest of finding any kind of glory in doing so.