Sinusoidal waves and Maxwell eqns

In summary, the conversation discusses the concept of a linear restoring force in simple harmonic motion and how it relates to Maxwell's equations. The restoring force in Maxwell's equations is attributed to the physical connection between the E and B fields, which results in simple harmonic motion. The Helmholtz equation is also mentioned as resembling the equation for spatial simple harmonic oscillators.
  • #1
fisico30
374
0
hello!,

question about Maxwell equations:

a linear restoring force causes simple harmonic motion. In Maxwell equations, what is this restoring force due to? In mechanics to mass and stiffness. do self inductance and capacitance the inertia and the stiffness?
HElmholtz eqn resembles the equation for the spatial simple harmonic oscillator.

thanks!
fisico30
 
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  • #3
Hi fisico30! :smile:
granpa said:
the springiness of space.

Yeah … and lambs gambol around the fields because of the springiness of time! :rolleyes:
fisico30 said:
a linear restoring force causes simple harmonic motion. In Maxwell equations, what is this restoring force due to? In mechanics to mass and stiffness.

do self inductance and capacitance the inertia and the stiffness?
HElmholtz eqn resembles the equation for the spatial simple harmonic oscillator.

I think it's basically because Maxwell's equations show that the two fields are reacting against each other … the E field pulls the B field, and vice versa …

curl E ~ -∂B/∂t, and curlB ~ ∂E/∂t …

and this physical connection between the fields gives the shm. :smile:
 
  • #4
tiny-tim said:
Hi fisico30! :smile:

I think it's basically because Maxwell's equations show that the two fields are reacting against each other … the E field pulls the B field, and vice versa …

curl E ~ -∂B/∂t, and curlB ~ ∂E/∂t …

and this physical connection between the fields gives the shm. :smile:

and? I think the op already knew that much. he's asking where the 'restoring force' comes from.
 

1. What are sinusoidal waves?

Sinusoidal waves are a type of wave that can be described by a sine or cosine function. They are characterized by their amplitude, frequency, and wavelength.

2. What are Maxwell's equations?

Maxwell's equations are a set of four equations that describe the behavior of electromagnetic fields. They were developed by James Clerk Maxwell in the 19th century and are fundamental to our understanding of electricity and magnetism.

3. How are sinusoidal waves related to Maxwell's equations?

Sinusoidal waves are a solution to Maxwell's equations. This means that they accurately describe the behavior of electromagnetic fields in a variety of situations, making them an important tool in understanding and predicting electromagnetic phenomena.

4. What is the significance of the speed of light in Maxwell's equations?

The speed of light, denoted by the letter c, is a fundamental constant in Maxwell's equations. It represents the speed at which electromagnetic waves propagate through a vacuum and is an important value in many areas of physics.

5. How are Maxwell's equations used in practical applications?

Maxwell's equations have a wide range of practical applications, including the design of antennas, electronics, and communication systems. They are also used in medical imaging, radar technology, and many other fields where the behavior of electromagnetic fields is important.

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