ElectricElectric ForcePolarizationInsulatorElectric Field of Charged RodElectric Field of Charged Ring, Disk, and PlaneElectric Field of Charged Spherical Shell Draft for Information Only
ContentEnergy of a Single Particle
Energy of a Single ParticleThe energy of a single particle is𝐸_{particle}=
Energy Principle for a Particlework done on particle=∆𝐸_{particle}=𝑊=
Assume rest energy does not change
∆𝐸_{particle}=𝑊=∆𝐾
Potential EnergyPotential energy is an interaction energy.∆𝐸_{1}=𝑊_{on,1}=
Consider the two particles as a system. internal work happens when the system changes shape. Potential energy is the interaction energy in a system of more than one particle. Therefore potential energy does not exist for a single particle system.
∆(𝐸_{1}+𝐸_{2})=𝑊_{surr}+𝑊_{internal} Total change in single particle energies
∆(𝐸_{1}+𝐸_{2})=∆𝐾=𝑊_{surr}+𝑊_{internal}
𝑊_{internal}+∆𝐾=𝑊_{surr}
∆𝑈+∆𝐾=𝑊_{surr} Multiparticle energy principle
⇒∆𝑈=−𝑊_{internal}
WorkThe work done on charge particle 𝑞_{2} to against the influence due to 𝑞_{1} is𝑊_{𝑎,𝑏}=
Electric Potential EnergyAccording to ∆𝑈=−𝑊_{internal}, the energy difference of a charged partcle in different position is equal to the difference of electric potential energy at different position with respect to the relative postion of the system. In other words, the electric potential energy between two charged particles can be expressed asElectric Potential Energy 𝑈=
Assume 𝑣_{𝑓}−𝑣_{𝑖}. Then ∆𝐾=0. Doing work on the system increases its potential energy. Work always changes 𝐸_{sys}, so the potential energy must have changed. The electric potential energy is similar to gravitational potential energy
For multiple electric charges
The electric potential energy of the system is
𝑈_{ele}=
Source and Referencehttps://www.youtube.com/watch?v=uUoR3DDwmo&list=PLZ6kagz8q0bvxaUKCe2RRvU_h7wtNNxxi&index=8 ©sideway ID: 191103002 Last Updated: 11/30/2019 Revision: 0 Latest Updated Links

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