# Radiative reaction Force From conservation of Energy

11. Aug 2020
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### Radiative reaction Force From conservation of Energy

• 1. Radiative reaction force from conservation of energy Represented by Maria Ashraf Roll#19011710-008 Department of Physics H-H Campus 1
• 2. Contents • Introduction • Law of Conservation of Energy • Radiative reaction force • Calculation of Radiative reaction force from conservation of energy • Conclusion • Recent work 2
• 3. Energy is the ability to do some sort of work….. 3 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. 4
• 5. Example 5 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. 6
• 7. 7 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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• 11. 11 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. 12
• 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. 13
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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. 15
• 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) 16
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