Electromagnetic Wave in Different Way

I want to ask a naïve question to everyone today. What’s the best way for learning?  I believe most of you will agree with me that it’s only during teaching when you understand whether you have understood the subject properly or not. If you teach someone and see that you fail to put yourself in his or her shoes, then be sure that there is a missing dot in your own learning or understanding of the subject. Recently, I got same kind of experience when I was teaching my son, a student of high school, on electromagnetic waves. He simply asked me how an electromagnetic wave can transmit energy to a charged particle during its propagation. I tried hard to explain it to him, but he was not satisfied at all. Hence, I was not. I could sense that I was missing something in my own understanding, which led me to using some jargons which were adding further confusion. Immediately, I decided to make a bee line to the R&D and came out with a fascinating conclusion that I can’t help but share with all of you with the fullest of ecstasy as follows.

Let’s understand at first what an electromagnetic wave is. When a charged particle e.g. electron is accelerated, the Electric Field produced by it changes over time, which induces a time-varying Magnetic Field, as per Modified Ampere’s Law. The time-varying Magnetic Field, in turn, produces an alternating Electric Field, as per Faraday’s Law. Thus, both type of fields continues to strengthen each other and propagates in the space as a combination named as Electromagnetic Wave with oscillating perpendicular to each other. The direction of propagation, the oscillation of Electric Field and Magnetic Field remain perpendicular to each other, as shown in Fig A below.

Now, let’s see the relationship between Electric Field and Magnetic Field in an Electromagnetic Wave.

From Maxwell’s Equations, we get B = E / C,

 where B = Magnetic Field, E = Electric Field, C= Velocity of Light

We understand from the above equation that B is much lesser that E due to high value of C in denominator.

Hence, in an Electromagnetic Wave, Magnetic Field is much weaker than its Electric Field.

Now, let’s understand how energy is transmitted by an Electromagnetic Wave during its propagation.

Let’s assume that the EM wave is propagating along the X-axis, Electric Field (E) is oscillating in the Y-axis and Magnetic Field (B) is oscillating in the Z-axis. (see Fig A)

When an EM wave propagates, any charged particle, say an electron in the space, will be deflected along the Y-axis with an oscillating motion due to the alternating values of the Electric Field along the Y-axis. Now, the Magnetic Field will create a force on this moving electron in the direction of propagation, as per Lorentz Force Law. Please see Fig B.

Similarly, the Magnetic Field will impart force on other electrons of the concerned particle resulting in the movement of the particle in the direction of the propagation.

In other words, it’s the Magnetic Field which transfers momentum to the particle, though it’s very weak part of an EM wave.

Let’s check the above statement with the equation derived from Lorentz Force Law.

F (b) = q x V x B

Where, F (b) = Force by Magnetic Field on the electron

               q = Charge of electron

              V = Velocity of electron due to Electric Field

              B = Magnetic Field

If we replace B by E/C, then we get,

F (b) = (q x V x  E) / C = (q x E x V) / C

Now, q x E = Force by Electric Field on the electron = F (e)

Hence, the above equation can be rewritten as

F (b) = (F (e) x V) / C

Now, Force x Velocity = Force x Distance / Sec = Energy Transfer by the Force / Sec.

Hence, F (e) x V can be termed as the Energy Transfer to the electron by the Electric Field per Sec.

It means that Energy Transfer to the particle takes place by the Electric Field since it’s the stronger part of an EM wave.

Now, we can express the above equation as below:

F (b) = (Energy Transfer to the electron by the Electric Field per Sec) / C

Now, Force = Momentum Transfer by the Force per Sec

Hence, F (b) = Momentum Transfer to the electron by Magnetic Field per Sec

Now, we can write the above equation as:

Momentum Transfer to the electron by Magnetic Field per Sec = (Energy Transfer to the electron by the Electric Field per Sec) / C

Cancelling per Sec at both sides, we get,

Momentum Transfer to the electron by Magnetic Field = (Energy Transfer to the electron by the Electric Field) / C

If we assume,

P = Momentum Transfer, and E = Energy Transfer, then,

P = E / C

Now, let’s cross-check the above conclusion with the equation of Energy, as was already derived in my earlier article.

The equation is:

E2 = (PC)2 + (MC2)2, where M = Mass

Since, the Mass of Electromagnetic Wave is zero i.e. M = 0, the above energy equation for an Electromagnetic wave is reduced to as

E = PC

or, P = E / C

Wow!!!  Our derivation is validated.

Now, let me summarize the above conclusions regarding an Electromagnetic Wave as below:

1.       The Magnetic Field is much weaker than the Electric Field.

2.       The relationship between Magnetic Field (B) and Electric Field (E) is B = E / C

3.       The Electric Field transfers the Energy whereas the Magnetic Field transfers the Momentum.

4.       The relation of Momentum Transfer (P) and Energy Transfer (E) is P = E / C

Did you think that way? Frankly Speaking, I did not.

That’s why teaching gives us so much of learning.

 Is not it?

EM Wave