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Consider, as a classical model of an electron, a uniformly charged spherical shell with charge e and radius R, spinning with angular velocity w a) Compute the total energy contained in the electromagnetic fields. b) Compute the total angular momentum contained in the electromagnetic fields. If n is the electromagnetic momentum density, then rxn is the angular momentum density. c) According to Einstein, the rest energy of a particle is related to its rest mass by E=mc2. If one assumes that all the rest mass m is due to the energy of the electron's electromagnetic field computed in (a), compute the radius R of the electron d) Assuming that the total angular momentum computed in (b) is equal to the intrinsic angular momentum of the electron, h/2, compute the angular velocity w of the electron. e) Are your results in (c) and (d) physically reasonable for the electron?

Consider, as a classical model of an electron, a uniformly charged spherical shell with charge e and radius R, spinning with angular velocity w a) Compute the total energy contained in the electromagnetic fields. b) Compute the total angular momentum contained in the electromagnetic fields. If n is the electromagnetic momentum density, then rxn is the angular momentum density. c) According to Einstein, the rest energy of a particle is related to its rest mass by E=mc2. If one assumes that all the rest mass m is due to the energy of the electron's electromagnetic field computed in (a), compute the radius R of the electron d) Assuming that the total angular momentum computed in (b) is equal to the intrinsic angular momentum of the electron, h/2, compute the angular velocity w of the electron. e) Are your results in (c) and (d) physically reasonable for the electron?

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Consider, as a classical model of an electron, a uniformly charged spherical shell with charge e and radius R, spinning with angular velocity w a) Compute the total energy contained in the electromagnetic fields. b) Compute the total angular momentum contained in the electromagnetic fields. If n is the electromagnetic momentum density, then rxn is the angular momentum density. c) According to Einstein, the rest energy of a particle is related to its rest mass by E=mc2. If one assumes that all the rest mass m is due to the energy of the electron's electromagnetic field computed in (a), compute the radius R of the electron d) Assuming that the total angular momentum computed in (b) is equal to the intrinsic angular momentum of the electron, h/2, compute the angular velocity w of the electron. e) Are your results in (c) and (d) physically reasonable for the electron?
Transcribed Image Text:Consider, as a classical model of an electron, a uniformly charged spherical shell with charge e and radius R, spinning with angular velocity w a) Compute the total energy contained in the electromagnetic fields. b) Compute the total angular momentum contained in the electromagnetic fields. If n is the electromagnetic momentum density, then rxn is the angular momentum density. c) According to Einstein, the rest energy of a particle is related to its rest mass by E=mc2. If one assumes that all the rest mass m is due to the energy of the electron's electromagnetic field computed in (a), compute the radius R of the electron d) Assuming that the total angular momentum computed in (b) is equal to the intrinsic angular momentum of the electron, h/2, compute the angular velocity w of the electron. e) Are your results in (c) and (d) physically reasonable for the electron?
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