Magnetic field of a circular wave

In summary, the conversation discusses the consistency of using the equation \vec{H}=\frac{1}{\eta}\hat{k}\times \vec{E} for calculating the Poynting vector of an electromagnetic wave. The person mentions an example of a circular wave and provides an alternative equation for calculating the Poynting vector. The expert then explains the correct way to calculate the Poynting vector using complex representation.
  • #1
kediss
1
0
Hi !

Does [itex]\vec{H}=\frac{1}{\eta}\hat{k}\times \vec{E}[/itex] always suit an electromagnetic wave ?

Because I'm getting some inconsistency for a circular wave :confused:

For instance:
[itex]\vec{E}=E_0(\hat{e}_x+e^{j\frac{\pi}{2}}\hat{e}_y)e^{-jkz}[/itex] (propagating [itex]\hat{e}_z[/itex])
[itex]\Rightarrow\vec{H}=\frac{E_0}{\eta}(\hat{e}_y-e^{j\frac{\pi}{2}}\hat{e}_x)e^{-jkz}[/itex]

The poynting vector results:
[itex]\vec{S}=\vec{E}\times\vec{H}=\frac{E^2_0}{\eta}e^{-2jkz}(1+e^{j\pi})\hat{e}_z=\vec{0}[/itex] which is quite disconcerting :/

Thx a lot for your help !
 
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  • #2
Your expression is not circular wave. Actually, it is not a wave at all, it is not time-dependent.

However, neglecting prefactors and with fixed orthogonal E and H:
[itex]\vec{E} \propto (e_x - e_y)[/itex]
[itex]\vec{H} \propto (e_x + e_y)[/itex]

=> [itex]S_z = E_x H_y - E_y H_x \propto 1-(-1) = 2 \neq 0[/itex]
 
  • #3
I think that if you use complex representation, the Poynting vector is calculated as
S=1/2(E x H*) where the star means complex conjugate.
With this definition, the real part of S is the average power density.
 

1. What is a circular wave?

A circular wave is a type of electromagnetic wave that propagates outward from a central source in a circular pattern. It is also known as a spherical wave because it expands in all directions.

2. How is a magnetic field created in a circular wave?

A magnetic field is created in a circular wave through the movement of charged particles, such as electrons. As these particles move in a circular path, they create a magnetic field that is perpendicular to the direction of their motion.

3. What factors influence the strength of the magnetic field in a circular wave?

The strength of the magnetic field in a circular wave is influenced by the amplitude of the wave, the distance from the source, and the frequency of the wave. A higher amplitude, shorter distance, and higher frequency will result in a stronger magnetic field.

4. How is the direction of the magnetic field determined in a circular wave?

The direction of the magnetic field in a circular wave is determined by the right-hand rule. If you point your thumb in the direction of the electric field, your fingers will curl in the direction of the magnetic field.

5. What are some practical applications of the magnetic field of a circular wave?

The magnetic field of a circular wave has many practical applications, including in wireless charging, electromagnetic induction, and MRI machines. It is also used in various forms of communication, such as satellite transmissions and radio broadcasting.

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