Hertzian diople, magnetic field and relation to Maxwell's equations

In summary, a Hertzian dipole is a model used to describe the behavior of electromagnetic radiation, consisting of two equal and opposite charges oscillating along a line. It produces an electric field that creates a perpendicular magnetic field, and is important in verifying Maxwell's equations. The strength of the magnetic field is directly proportional to the size of the dipole. While Hertzian dipoles have been used in practical applications, they have largely been replaced by more advanced antenna designs.
  • #1
kings
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Homework Statement


Show how the given physical magnetic field is consistent with a monochromatic plane wave solution to Maxwell equation

Homework Equations


[/B]
Physical:
> Bphys(t) = B0 sin (2πft) ex

Maxwells:
> B = iB0 exp[i(kz − ωt)] ex.

The Attempt at a Solution


I know that field is the real part of maxwells equation but I am struggling to find how to can work out how to get from one to the other?
I also got that ω=2πf and k = ω/c
Am i heading the right direction?
 
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  • #2
What is i (##=\sqrt{-1}##) written in terms of an exponential?
 

1. What is a Hertzian dipole?

A Hertzian dipole is a hypothetical model used to explain the behavior of electromagnetic radiation. It consists of two equal and opposite charges oscillating back and forth along a line, creating an electric field that radiates energy in the form of electromagnetic waves.

2. How is a magnetic field related to a Hertzian dipole?

A Hertzian dipole produces an oscillating electric field, which in turn creates a perpendicular magnetic field. These two fields are interconnected and together make up an electromagnetic wave.

3. What is the significance of Hertzian dipoles in relation to Maxwell's equations?

Hertzian dipoles are important because they were used by Heinrich Hertz in his experiments to verify the existence of electromagnetic waves and confirm James Clerk Maxwell's theory of electromagnetism as described by his famous set of equations.

4. How does the size of a Hertzian dipole affect the strength of its magnetic field?

The strength of the magnetic field created by a Hertzian dipole is directly proportional to the size of the dipole. A larger dipole will produce a stronger magnetic field, while a smaller dipole will produce a weaker one.

5. Can Hertzian dipoles be used in practical applications?

While Hertzian dipoles are primarily used as a theoretical model, they have also been used in practical applications such as radio antennas and wireless communication devices. However, more efficient and complex antenna designs are now used in most modern technologies.

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