# Example for Poynting's Theorem

• shynee
In summary, the conversation revolved around the application of Poynting's Theorem and its relation to the conservation of energy in the electromagnetic field. The topic of laser tweezers was also brought up, with a question about its working mechanism and the parts of the equation involved. It was mentioned that laser tweezers use light scattering and momentum transfer to trap and maintain an object, or create a potential well for it. The conversation also touched on finding interesting problems to solve related to this topic.
shynee
Hi,

Anyone knows a good example to aply Poynting's Theorem?

The one thas defines the conversation of energy in the electromagnetic field?

Regards Martin

Laser tweezers?

Laser tweezer?

I don't have a clue, how they work.

Which parts of the Equaction are involved?

The integral of the Poyntig Vektors, and which more?

Absorbed sunlight, heating a surface.

shynee said:
Laser tweezer?

I don't have a clue, how they work.

Which parts of the Equaction are involved?

The integral of the Poyntig Vektors, and which more?

A laser tweezer maintains a trapped object by light scattering. Momentum from the light is transferred to the trapped particle. Alternatively, the focused beam of light creates a potential well for the particle.

There's lots of material out there- my understanding was that you were looking for an interesting problem to solve. Is that wrong?

## 1. What is Poynting's Theorem?

Poynting's Theorem is a fundamental law in electromagnetism that describes the relationship between the electric and magnetic fields in a region of space, and the flow of energy through that region. It was developed by English physicist John Henry Poynting in the late 19th century.

## 2. How is Poynting's Theorem used?

Poynting's Theorem is used to calculate the amount of energy carried by an electromagnetic field. It is also used to understand the direction and rate of energy transfer in a given system, such as in a circuit or electromagnetic wave.

## 3. What is the mathematical equation for Poynting's Theorem?

The mathematical equation for Poynting's Theorem is:
S = (1/μ0)(E x B)
where S represents the energy flux density, E is the electric field, B is the magnetic field, and μ0 is the permeability of free space.

## 4. How does Poynting's Theorem relate to the conservation of energy?

Poynting's Theorem is a statement of the conservation of energy in electromagnetic systems. It states that the total energy in a closed system remains constant, and any changes in energy are due to the flow of energy through the system.

## 5. What are some practical applications of Poynting's Theorem?

Poynting's Theorem has many practical applications, including in the design and analysis of electronic circuits, antennas, and electromagnetic devices. It is also used in understanding the behavior of electromagnetic waves, such as in telecommunications and radar systems.

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