Why is the field view preferable to the action-at-a-distance view of forces
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$$$${{{{{{{{{{. In classical electromagnetic theory one has both charged particles and the EM field. While state of a particle - its position and momentum - can be chosen freely, the state of the EM field is constrained a lot by the Maxwell equations, namely by the equations
∇⋅E=ρ,∇⋅E=ρ,
∇⋅B=0.∇⋅B=0.
Thus the field is not an entirely independent object to describe; it is partially dependent on the particles and thus its numerical representation is partially superfluous in describing the state of the system.
On the other hand, even with these restrictions, the fields can be chosen in an infinite number of ways and it is not immediately clear which initial and boundary conditions should be supplemented to the equations to solve for, say, the motion of the electron around the proton.
If the particles are points, which is the simplest case and electrons may be such according to current knowledge, this formulation with one field has also very serious problem that it is not capable to determine force acting on the charged particle (the field is singular at the position of all point particles). This lead to great confusion about the equation of motion of a charged particle - see the most famous attempt, so-called Lorentz-Abraham-Dirac equation, which has serious problems though.
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^_^:-(:-(:-(:-(:-(:-(:-(:-(Your answer :-):-):-):-):-):-):-):-):-)::-):-)
$$$${{{{{{{{{{. In classical electromagnetic theory one has both charged particles and the EM field. While state of a particle - its position and momentum - can be chosen freely, the state of the EM field is constrained a lot by the Maxwell equations, namely by the equations
∇⋅E=ρ,∇⋅E=ρ,
∇⋅B=0.∇⋅B=0.
Thus the field is not an entirely independent object to describe; it is partially dependent on the particles and thus its numerical representation is partially superfluous in describing the state of the system.
On the other hand, even with these restrictions, the fields can be chosen in an infinite number of ways and it is not immediately clear which initial and boundary conditions should be supplemented to the equations to solve for, say, the motion of the electron around the proton.
If the particles are points, which is the simplest case and electrons may be such according to current knowledge, this formulation with one field has also very serious problem that it is not capable to determine force acting on the charged particle (the field is singular at the position of all point particles). This lead to great confusion about the equation of motion of a charged particle - see the most famous attempt, so-called Lorentz-Abraham-Dirac equation, which has serious problems though.
}}}}}}}$$$$$$$$
£££££&&&&&&&&&&+££Hope Help your ££££££&&&&&&&&&+£££?
?
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