Does a charge radiate only when changing direction?

In summary: To calculate the energy, you would need to multiply the power by time. In summary, an electron accelerating in a straight line will radiate energy, but the rate of radiation depends on the direction of acceleration. In the case of an electron orbiting a nucleus, the necessary energy to compensate for bremsstrahlung can be calculated using the Larmor formula, but it is important to note that this formula gives a radiated power, not an energy.
  • #1
alba
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They say that an electron accelerating radiates and loses energy, and that is one of the reasons why an electron cannot orbit a nucleus:

- 1) does a charge accelerating in a straight line radiate, and what is the rate of radiation? do we have to supply extra Ke (apart from m/2 v^2) when we accelerate an electron?

- 2) Ke in the ground state of hydrogen is 13.6 eV, what energy per second should we supply anelectron to keep it in orbit,? I tried to apply the formula at wiki, but I get 1 Tera eV
 
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  • #2
alba said:
- 2) Ke in the ground state of hydrogen is 13.6 eV, what energy per second should we supply anelectron to keep it in orbit,? I tried to apply the formula at wiki, but I get 1 Tera eV

None. The electron in the ground state is already in a stable orbital and cannot drop down any further. Note that classical E&M rules don't apply at the atomic level. For that you need Quantum Mechanics.
 
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  • #3
I am referring to the classical model, of course. I'd like to know how much extra energy is necessary to compensate the bremsstrahlung.

My main question, anyway, concerns an accelerating charge in a straight line, does it radiate?
 
  • #4
alba said:
I am referring to the classical model, of course. I'd like to know how much extra energy is necessary to compensate the bremsstrahlung.

My main question, anyway, concerns an accelerating charge in a straight line, does it radiate?
Why not?
Fast charged particles can be brought to a halt when they enter a solid mass and they release high energy radiation. That would involve 'linear' (negative) acceleration over a very short time (/ distance). I can't think of a mechanism that would produce positive acceleration with as high a value - except in nuclear reactions. But that would instantly take you into the realms of non-classical Physics.
But you seem to be requiring an 'unhealthy' mix of Classical and QM, which usually means tears before bed time. :smile:
 
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  • #5
sophiecentaur said:
Why not?
But you seem to be requiring an 'unhealthy' mix of Classical and QM, which usually means tears before bed time. :smile:

No, I am simply asking what happens when you accelerate (not decelerate) an electron.
Also, I am asking, if a charge circles a nucleus with 13.6 eV Ke , how much energy is needed to compensate bremsstrahlung. According to Larmor formula it should exhaust its Ke in 10^-11 seconds., but I think it is naive to multiply 13.6 by 10^11. That's how I got 1 Tera eV. Did you get that?
 
  • #7
alba said:
what happens when you accelerate (not decelerate) an electron.
There is no difference. It's the same thing in different frames.
 
  • #8
It seems like you are confusing energy and power. Larmor formula gives a radiated power, not an energy.
 

1. What is meant by a charge radiating when changing direction?

A charge radiating when changing direction refers to the emission of electromagnetic radiation by a charged particle when it changes its direction of motion. This phenomenon is also known as acceleration radiation or bremsstrahlung.

2. Does a stationary charge radiate?

No, a stationary charge does not radiate. According to Maxwell's equations, a changing electric field is required for electromagnetic radiation to be emitted. Since a stationary charge does not have a changing electric field, it does not radiate.

3. How does the acceleration of a charge affect the amount of radiation emitted?

The amount of radiation emitted by a charge is directly proportional to its acceleration. This means that the faster a charge accelerates, the more radiation it will emit.

4. Are all types of charges capable of radiating when changing direction?

Yes, all types of charges, whether positive or negative, can radiate when changing direction. This is because the emission of electromagnetic radiation is a fundamental property of charged particles.

5. Is there a limit to the frequency of radiation emitted when a charge changes direction?

Yes, there is a limit to the frequency of radiation emitted when a charge changes direction. This limit is known as the cutoff frequency and it depends on the mass and velocity of the charged particle. Any radiation emitted with a frequency above the cutoff frequency is known as high-energy radiation.

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