# Accelerating charged particles and conservation of energy

• dgnunch
In summary, when a charged particle is accelerated, it emits energy in the form of em radiation while also gaining kinetic energy.
dgnunch
Hi I'm wondering how when a charged particle is accelerating it both emits energy in the form of em radiation while also gaining kinetic energy. All of that energy comes from the thing accelerating the charged particle, yeah? Is that necessary, like it is not possible to give a charged particle kinetic energy without letting it "donate" some of it to the em radiation? Conservation of energy in terms of both the sun emitting energy via nuclear fusion and "bremsstrahlung" make sense to me.. but what dictates how much energy gets donated to the em waves and how much to kinetic? Like it seems arbitrary?

berkeman
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sophiecentaur
dgnunch said:
Hi I'm wondering how when a charged particle is accelerating it both emits energy in the form of em radiation while also gaining kinetic energy. All of that energy comes from the thing accelerating the charged particle, yeah?
Yes. The energy expended to accelerate a charged particle is the sum of the increase in kinetic energy and the energy that is radiated away.
Is that necessary, like it is not possible to give a charged particle kinetic energy without letting it "donate" some of it to the em radiation?
Not possible (at least not in the context of this thread). The electrical field around the particle must change when it is accelerated because we are moving a charged particle around. Electromagnetic radiation is the way that change propagates, so it has to be present.
Conservation of energy in terms of both the sun emitting energy via nuclear fusion and "bremsstrahlung" make sense to me.. but what dictates how much energy gets donated to the em waves and how much to kinetic? Like it seems arbitrary?
Calculating exactly how much energy goes into radiation and how much goes into kinetic energy change will depend on the details of your particular setup. But it's not arbitrary: if you say that we have a charged point particle moving with a given acceleration along a given path we can in principle calculate exactly what the radiation emission will be.

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davenn and berkeman
dgnunch said:
Like it seems arbitrary?
Not "arbitrary", surely. The theory will tell you just how the Energy is shared.
There are other, more homely, apparent paradoxes about Energy transfers - such as where the energy goes when you connect a charged capacitor to an uncharged capacitor of the same value. And why, however fast or slow you choose to charge a capacitor, you 'waste' as much energy as you have put into the capacitor.

berkeman

## 1. What is the purpose of accelerating charged particles?

The purpose of accelerating charged particles is to increase their kinetic energy and therefore their speed. This is important in many scientific and technological applications, such as particle accelerators used in physics research and medical devices like radiation therapy machines.

## 2. How does the conservation of energy apply to accelerating charged particles?

The law of conservation of energy states that energy cannot be created or destroyed, only transferred or converted. When charged particles are accelerated, their kinetic energy increases, but this energy comes from a source such as an electric field or magnetic field. Therefore, the total energy of the system (particles plus fields) remains constant.

## 3. Can charged particles be accelerated indefinitely?

No, charged particles cannot be accelerated indefinitely. Due to the conservation of energy, there is a limit to how much energy can be transferred to the particles. Once they reach a certain speed, they will not gain any more kinetic energy and will instead follow a straight path at a constant speed.

## 4. What factors affect the acceleration of charged particles?

The acceleration of charged particles is affected by several factors, including the strength of the electric or magnetic field, the charge and mass of the particles, and any resistive forces present in the system. The type of particle (positive or negative) also plays a role, as particles with opposite charges will accelerate in opposite directions.

## 5. How is the acceleration of charged particles measured?

The acceleration of charged particles can be measured using various instruments, such as particle detectors or spectrometers. These devices measure the energy and speed of the particles, which can then be used to calculate their acceleration. Additionally, the path of the particles can be observed and analyzed to determine their acceleration over time.

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