This document discusses the radiative reaction force from the perspective of the conservation of energy. It explains that when an external force accelerates a charged particle, the particle both gains kinetic energy from the work of the external force and radiates power according to Larmor's formula. For energy to be conserved, there must be an additional force, called the radiative reaction force, that does work to decrease the particle's energy change and transfer that energy to the radiated field. The document provides the equation that defines the radiative reaction force and explains how it ensures energy conservation. It concludes that considering the radiative reaction force satisfies the law of conservation of energy for systems that radiate energy when an external force is applied.

1. Radiative reaction force
from conservation of
energy
Represented by Maria Ashraf
Roll#19011710-008
Department of Physics
H-H Campus
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2. Contents
• Introduction
• Law of Conservation of Energy
• Radiative reaction force
• Calculation of Radiative reaction force from
conservation of energy
• Conclusion
• Recent work
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3. Energy is the ability to do some sort of
work…..
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The different types of
energy are following.
• Thermal energy
• Radiant energy
• Chemical energy
• Nuclear energy
• Electrical energy
• Motional energy
• Sound energy
• Elastic energy
• Gravitational energy

4. Law of conservation of energy
• Energy can neither be created nor be destroyed.
• Energy changes forms.
• Energy on a system remain conserved.
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5. Example
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Energy changes
from one form to
another form.

6. Why atoms gives of radiations?
• Stability of the nucleus determine.
• Balance between repulsive force and strong
nucleus force.
• Ratio of the proton to neutrons.
• Unstable nucleus gives of radiation.
• Atoms that do not have the ideal ratio of P:n will
gives of radiation to fix the ratio.
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Consider a charge particle p, if an external force ‘F’ applied on it, then
F=m𝑣.
According to Newton's 2nd Law for a charged particle being accelerated by a given
external force. The work energy theorem dictates how fast the particle can gain
kinetic energy if this is the only force acting. However, at the same time it is being
acted on by the external force (and is accelerating), it is also radiating power
away at the total rate:
P=
2 𝑒2
3×4π∈0 𝑐3 𝑣.2
This also called larmor formula.
P=
2 𝑚𝑟𝑒
3 𝐶
𝑣.2
P=m𝜏 𝑟 𝑣.2
Calculation of Radiative reaction force
from conservation of energy

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According to the conservation of energy, the work done by the external force
must equal the increase in kinetic energy plus the energy radiated into the
field. Energy conservation for this system states that:
𝑊𝑒𝑥𝑡 = ∆𝐸𝑒 + ∆𝐸𝑓
𝑊𝑒𝑥𝑡 − ∆𝐸𝑓 = ∆𝐸𝑒
there must be another force acting on the electron, one where the total work
done by the force decreases the change in energy of the electron and places
the energy into the radiated field. We call that force 𝐹𝑟𝑎𝑑 the radiative
reaction force.
𝐹𝑟𝑎𝑑 + 𝐹𝑒𝑥𝑡 = 𝐹 𝑡𝑜𝑡𝑎𝑙
𝐹𝑟𝑎𝑑 = 𝑚𝑣. − 𝐹𝑒𝑥𝑡
This equation
defines the radiative reaction force that must act on the particle in order for
energy conservation to make sense.
Explanation

12. The reaction force has a number of
desirable properties
• We would like energy to be conserved, so that the
energy that appears in the radiation field is balanced
by the work done by the radiative reaction force.
• This force become vanish when the external force
vanishes, so that particles do not spontaneously
accelerate away to infinity without an external agent
acting on them.
• Finally, force involve the characteristic time (t) since
no other time-scaled parameters are available.
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13. We want the energy radiated by some `bound' charge must
be equal to the work done by the radiation reaction force.
in the previous equation. Let's start by examining just the
reaction force and the radiated power.
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15. Conclusion
• All the systems radiate its energy when the
external force is applied it. If we sum up this
radiating force with the work done by the
systems then its satisfy Law of conservation of
energy.
• Since total energy of the system remain
conserved.
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16. Recent work on Energy conservation
• MITCON consultancy & Engineering Services
working on the Green Power and Energy
conservation.
• Energy efficiency and energy conservation
company in USA.
• Environmental and Energy institute
Washington.
• DEXMA company work and invest in Energy
Conservation Measures (ECMs)
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17. Any question
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