# Impulse of electromagnetic field

• Petar Mali
In summary, the conversation discusses the total field law of conservation of impulse and how it relates to the law of action and reaction in electrodynamics. It is mentioned that \int_V\vec{g}dV=\vec{const} is necessary but not always sufficient for this law. The question is then posed, when is \int_V\vec{g}dV=\vec{const} a necessary and sufficient condition for this law? The answer is not obvious and further discussion is needed.
Petar Mali
We have

$$\vec{F}=\int_V\vec{f}dV=-\frac{d}{dt}\int_V(\vec{D}\times \vec{B})dV$$

$$\vec{g}=\vec{D}\times \vec{B}$$

$$\vec{F}=-\frac{d}{dt}\int_V\vec{g}dV$$

$$\vec{F}=\frac{d\vec{p}_{mech}}{dt}$$

$$\frac{d}{dt}(\vec{p}_{mech}+\int_V\vec{g}dV)=0$$

$$\vec{p}_{mech}+\int_V\vec{g}dV=\vec{const}$$

In total field law of conservation of impulse

$$\vec{p}_{mech}$$ - mechanical impulse of particles in field

In one book I found that $$\int_V\vec{g}dV=\vec{const}$$ is necessary but not always sufficient condition for law of action and reaction in electrodynamics.

My question is when is $$\int_V\vec{g}dV=\vec{const}$$ necessary and sufficient condition for this law? Thanks for your answer!

Does anyone know this?

Petar Mali said:
$$\vec{p}_{mech}+\int_V\vec{g}dV=\vec{const}$$

In total field law of conservation of impulse

$$\vec{p}_{mech}$$ - mechanical impulse of particles in field

In one book I found that $$\int_V\vec{g}dV=\vec{const}$$ is necessary but not always sufficient condition for law of action and reaction in electrodynamics.

My question is when is $$\int_V\vec{g}dV=\vec{const}$$ necessary and sufficient condition for this law? Thanks for your answer!

If you believe
$$\vec{p}_{mech}+\int_V\vec{g}dV=\vec{const}$$,
then isn't the answer obviously, yes?
I assume you mean NIII for the forces on objects.

NIII?

No! It's not obviously, I think. What is your idea?

I would like to first clarify that the equations and concepts mentioned in the content are related to the dynamics of electromagnetic fields, specifically the relationship between force, impulse, and the law of conservation of impulse. This is an important topic in the field of electromagnetism and has been extensively studied and verified through experiments.

To answer your question, the condition \int_V\vec{g}dV=\vec{const} is necessary and sufficient for the law of action and reaction in electrodynamics when the electromagnetic fields are in a steady state. In other words, when the fields are not changing with time and there are no external forces acting on the system, the law of conservation of impulse holds true and the total impulse of the system remains constant.

However, when the fields are not in a steady state and are changing with time, the condition \int_V\vec{g}dV=\vec{const} may not be sufficient for the law of action and reaction to hold. This is because in such cases, the total impulse of the system may not remain constant due to the presence of external forces or the emission of electromagnetic waves. In these scenarios, additional terms may need to be considered in the equation to fully account for the dynamics of the system.

In conclusion, the condition \int_V\vec{g}dV=\vec{const} is necessary and sufficient for the law of action and reaction in electrodynamics only in the case of steady state fields. In other cases, further considerations and calculations may be needed to accurately describe the behavior of the system.

## What is the impulse of an electromagnetic field?

The impulse of an electromagnetic field is a measure of the change in momentum of charged particles when they interact with the field. It is a vector quantity that describes the force and direction of the change in motion.

## What factors affect the impulse of an electromagnetic field?

The impulse of an electromagnetic field is affected by the strength and direction of the field, as well as the charge and velocity of the particles interacting with the field.

## How is the impulse of an electromagnetic field calculated?

The impulse of an electromagnetic field is calculated by multiplying the force experienced by the charged particle by the time interval during which the force is applied. This can be represented mathematically as J = FΔt.

## What are some real-world applications of the impulse of an electromagnetic field?

The impulse of an electromagnetic field has many applications, including in particle accelerators, electric motors, and generators. It is also crucial in understanding the behavior of charged particles in space and the creation of electromagnetic radiation.

## How does the impulse of an electromagnetic field relate to other concepts in physics?

The impulse of an electromagnetic field is closely related to concepts such as electric and magnetic fields, force, and momentum. It is also an important component of the study of electromagnetism and the behavior of charged particles in various environments.

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