# E field - B field interaction

• trini
In summary, the conversation discusses the possibility of generating visible light inside a box by pulsing both electric and magnetic fields at visible light frequency. However, it is mentioned that the fastest antennas we currently have are only effective in the terahertz range, which is still much lower than visible light frequency. The conversation also delves into the theoretical aspects of electromagnetic fields and their interaction, and it is concluded that the frequency of electromagnetic waves generated by this mechanism is limited to wavelengths comparable to the size of the circuit elements. Therefore, it is unlikely that the proposed setup would be able to generate visible light, even if technical issues were overcome.

#### trini

Ok so I was wondering, let's say I have a device (eg., shaped like a toothpaste box with the two square ends cut off). I make 2 of the opposite faces from copper plate and the other 2 from iron plate (for example). I then generate an electric field in the box with the copper plates, and a magnetic field from the iron plates. If I pulse both the E and B fields at visible light frequency, will the result be visible light in the box?

What you are basically constructing is an antenna. I don't believe there are any antennas capable of generating/receiving frequencies as high as visible light. Your setup would probably have VERY high impedance for frequencies that high, so it wouldn't work.

The 'fastest' antenas we have are 'nanotube' antennas, which are effective in the terahertz (10^12 Hz), which is still much lower than visible light (10^15 Hz).

its a thought experiment, assume we get past technical issues.

Okay, but you still mention copper/iron, which wouldn't react fast enough to an applied voltage to achieve these frequencies. :uhh:

But, if you could construct some antenna which can achieve frequencies high enough, you would see light.

thats awesome, it means if we ever get there we can have light sources with incredible bandwidth and resolution. photochemistry would never be the same.

You don't need a separate magnetic field source. A variable electric field induces a magnetic field, according to Ampere-Maxwell's Law, which in integral form is:
$$\oint_{C}{\vec{B} \cdot d\vec{\mathcal{l}}} = \frac{1}{c^2} \, \frac{\partial}{\partial t} \left( \, \iint_{S}{(\vec{E} \cdot \hat{n}) \, da} \right) + \mu_0 \, I$$
where C is a closed contour with a line element $d\vec{\mathcal{l}}$, and S is any surface subtended on the contour C with a unit normal $\hat{n}$. I is the total (convective) electric current passing through the contour C.

In vacuum, the convective current I is zero, but the displacement current (the first term on the r.h.s. containing a time derivative of the electric flux) is usually large due to a rapidly oscillating field.

This (osillating) magnetic field, in turn, generates additional electric fields, according to Faraday's Law:
$$\oint_{C}{\vec{E} \cdot d\vec{\mathcal{l}}} = -\frac{\partial}{\partial t} \left( \iint_{S}{(\vec{B} \cdot \hat{n}) \, da}\right)$$

This is essentially the mechanism for emitting electromagnetic waves that propagate freely in space away from the initial source of the oscillating electric field.

However, as mentioned by other posters, the frequency of electromagnetic waves generated by this mechanism is limited to frequencies that correspond to a wavelength comparable to the linear dimensions of the circuit elements.

indeed, the only reason i suggest both is to have increased control over the photon's EM vector

trini said:
indeed, the only reason i suggest both is to have increased control over the photon's EM vector

But, you will not have because the two fields will be incoherent, thus forming independent electromagnetic waves.

## 1. How do electric and magnetic fields interact with each other?

Electric and magnetic fields are both components of the larger electromagnetic field. They interact with each other through a phenomenon called electromagnetic induction, where changes in one field can induce a corresponding change in the other field.

## 2. What is the significance of the E field - B field interaction in everyday life?

The E field - B field interaction is responsible for many everyday technologies, such as electricity and magnetism-based devices like generators and motors. It also plays a crucial role in electromagnetic radiation, which includes radio waves, microwaves, and visible light, making it essential for communication, transportation, and entertainment.

## 3. How does the E field - B field interaction relate to Maxwell's equations?

Maxwell's equations are a set of mathematical equations that describe the behavior of electromagnetic fields. The E field - B field interaction is a fundamental aspect of these equations and is essential for understanding the behavior of electromagnetic waves and fields.

## 4. Can the E field and B field exist independently of each other?

No, the E field and B field are interconnected and cannot exist independently. Changes in one field will always affect the other field, and they are both necessary for the existence and propagation of electromagnetic waves.

## 5. How is the E field - B field interaction used in scientific research?

The E field - B field interaction is a crucial concept in many areas of scientific research, including particle physics, astrophysics, and material sciences. It is used to study the behavior and manipulation of electromagnetic fields and their effects on matter, allowing scientists to better understand the fundamental forces of nature.