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

 

Electromagnetic Nature of Light — A brief history of light Reply

“Electromagnetic Nature of Light — A brief history of light” This lecture was delivered on 16th March, yesterday, in a lecture session of 1 and 1/2 hours. The second part of this lecture was delivered to Physics honors as well as Physics elective students.

As I promised in the last lecture, lecture-X we have our one of the interesting historical and technical perspective about light that is also one of my favorite, as I discovered yesterday, or shortly before that, the night before, when I was composing the lecture from scratch. We will name this lecture with its proper number, only after its clear to us what chronological number it must be associated with it. Its like an advanced wave, it reached us before in time, before it was intended to be taken up for its web-version.

Let us begin this lecture which has roughly two parts, 1. the history of light and its understanding through the centuries and 2. the electromagnetic nature of light. The second part is intended as the course material for honors as well as elective students but you will be in amusement if you also cover the first part.

A brief history of light.

Various optical devices and optical phenomena have been known since close to 4000 years. The optical devices of ancient time includes mirrors, burning glasses, lenses and other magnifying devices.

Accordingly various properties and laws of light were understood and developed since these times. Eg light was understood to propagate rectilinearly, light was understood to reflect and refract. There were various laws that were known since these times which catered to the need for explanation of these phenomena. eg Reflection was understood to be a phenomena explained by the principle of shortest path — follow link to know this and other related ideas and their history: Hero of Alexandria. Laws of refraction were understood either partially or completely as the centuries or even millennia passed.

Apart from rectilinear propagation of light it was understood that light moves at infinitely large speed. Advanced optical devices such as telescopes were developed based on partial and faulty understanding of light which was gradually refined to accommodate better credits of advancement. More…

Interference of two plane harmonic waves. 7

Optics Series Lecture, Lecture – VII.

“Conditions of interference, Interference of two plane harmonic waves.” This lecture was delivered on 7th February in a lecture session of 1 and 1/2 hours. This lecture was delivered to Physics elective students but intended as a lecture towards Honors students at a later date.

Electromagnetic Waves.

Light is an electromagnetic wave. In-fact its a transverse electromagnetic wave which means the oscillation of E and B fields produces light which propagates in a direction that is perpendicular to the plane that contains the E and B fields. In other words E, B and k the vector that denotes the direction of light propagation, are mutually perpendicular vectors. We will study these details in a later intended lecture. EM waves are not only transverse waves but also vector waves, that is; E and B are vector fields whose undulation is summarized as light.

Light is a general name for all EM waves but visible light is that particular part of EM waves which has frequency of wave such that the wavelength varies from approximately 400 – 700 nm. In vacuum — only in vacuum, light always moves at a fixed speed: namely 3×108 m/s. Therefore light whose wavelength lies between 400 – 700 nm is called as visible light: we can write in vacuum c = νλ.

Light as a transverse wave phenomenon of vector fields is comprehensively described by four equations known as Maxwell’s Equations. More…

The Maxwell’s Equations, from nature to instruments. 1

The beauty of Maxwell’s equations can be seen in how it helps us understand nature as well as instruments, at the same time. Medical devices are simply an advanced understanding that began with understanding electromagnetic waves through Maxwell’s equations.

Each of the following 4 equations has a different name, by which we call’em, but together they are called as the Maxwell’s equations. Together they constitute what I am inspired to say; the golden equations of Physics. If we do some easy tricks they will be converted into whats called as the Wave Equations (of motion) ! Yes, they describe the wave behavior “fully”.

— By that I don’t mean sound waves, but any sort of waves that move at the speed of light. Sound waves are ordinary pressure oscillations, that travel much slower than even rockets.
The 4 equations therefore describe how electromagnetic waves are created and broadcast. Hence TV radio and satellite communication were understood because these 4 equations were understood.

First two are time-independent or static equations.

The first equation is known as Gauss’s law of electrostatics and says “Electric fields (E), are a result of sources of electrostatic charge”.

The 2nd equation is analogous and called as Gauss’s law of static magnetic field. But it says “apparently there are no sources of magneto-static charge or single magnetic pole from which the magnetic field B is created”.

Then how are magnetic fields created? We needed to know further to find the answer. Lets look at the 3rd and 4th equations. More…