Feynman’s disk paradox

Lombardi, Gabriel G.

doi:10.1119/1.13272

Cited by 18 publications

(10 citation statements)

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“…This variant of Feynman's disk paradox was first proposed by Romer[2] and Boos[3]; the original paradox is discussed in Sec. 17.4 of Volume II of the Feynman lectures[4], and in Ref [5]…”

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confidence: 99%

Self-torque and angular momentum balance for a spinning charged sphere

Bonga

Poisson

Yang

2018

American Journal of Physics

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Angular momentum balance is examined in the context of the electrodynamics of a spinning charged sphere, which is allowed to possess any variable angular velocity. We calculate the electric and magnetic fields of the (hollow) sphere, and express them as expansions in powers of τ /tc ≪ 1, the ratio of the light-travel time τ across the sphere and the characteristic time scale tc of variation of the angular velocity. From the fields we compute the self-torque exerted by the fields on the sphere, and argue that only a piece of this self-torque can be associated with radiation reaction. Then we obtain the rate at which angular momentum is radiated away by the shell, and the total angular momentum contained in the electromagnetic field. With these results we demonstrate explicitly that the field angular momentum is lost in part to radiation and in part to the self-torque; angular momentum balance is thereby established. Finally, we examine the angular motion of the sphere under the combined action of the self-torque and an additional torque supplied by an external agent.

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“…This variant of Feynman's disk paradox was first proposed by Romer[2] and Boos[3]; the original paradox is discussed in Sec. 17.4 of Volume II of the Feynman lectures[4], and in Ref [5]…”

mentioning

confidence: 99%

Self-torque and angular momentum balance for a spinning charged sphere

Bonga

Poisson

Yang

2018

American Journal of Physics

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“…The conservation of linear and angular momenta of charges in the presence of a changing magnetic dipole, an idealized version of the Feynman disc paradox, is explicitly demonstrated. 4 An alternative way of deriving this result is to note that changing the magnetic dipole induces an electric field E MF , which imparts an impulse P Q = Q dt E MF (r, t ) on the charge Q at r. The electromagnetic fields due to the dipole can be represented by a vector potential A(r, t ) in the Coulomb (∇ · A = 0) gauge, in which case the scalar potential caused by the changing magnetic dipole is zero. Hence, the electric field is E MF = −∂A/∂t and the impulse on the charge q is [7] P Q = −Q dt ∂A ∂t = −Q A.…”

Section: Discussionmentioning

confidence: 99%

“…This paradox is resolved when the angular momentum of the electromagnetic field around the solenoid is taken into account. However, Feynman in his Lectures in Physics [1] did not quantitatively show that the angular momentum contained in the electromagnetic field is equal to the angular momentum imparted to the charge, perhaps because explicitly calculating the electromagnetic momentum is not easy [3][4][5][6]. Furthermore, students who first encounter this paradox typically attempt erroneously to explain it by claiming that the angular momentum of the charge carriers which carry the current in the solenoid is transferred to the ring of charges.…”

Section: Introductionmentioning

confidence: 99%

Introducing electromagnetic field momentum

2012

Eur. J. Phys.

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I describe an elementary way of introducing electromagnetic field momentum. By considering a system of a long solenoid and line charge, the dependence of the field momentum on the electric and magnetic fields can be deduced. I obtain the electromagnetic angular momentum for a point charge and magnetic monopole pair partially through dimensional analysis and without using vector calculus identities or the need to evaluate integrals. I use this result to show that linear and angular momenta are conserved for a charge in the presence of a magnetic dipole when the dipole strength is changed.

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“…For detailed analysis of the original version of Feynman's angular momentum paradox, see Ref. [15] for example. Here, let us discuss a simplified version of Feynman's angular momentum paradox.…”

Section: Feynman's Angular Momentum Paradox and Possible Relevance To...mentioning

confidence: 99%

Relativistic decomposition of the orbital and the spin angular momentum in chiral physics and Feynman's angular momentum paradox

Fukushima,

2020

Preprint

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Over recent years we have witnessed tremendous progresses in our understanding on the angular momentum decomposition. In the context of the proton spin problem in high energy processes the angular momentum decomposition by Jaffe and Manohar, which is based on the canonical definition, and the alternative by Ji, which is based on the Belinfante improved one, have been revisited under light shed by Chen et al. leading to seminal works by Hatta, Wakamatsu, Leader, etc. In chiral physics as exemplified by the chiral vortical effect and applications to the relativistic nucleus-nucleus collisions, sometimes referred to as a relativistic extension of the Barnett and the Einstein-de Haas effects, such arguments of the angular momentum decomposition would be of crucial importance. We pay our special attention to the fermionic part in the canonical and the Belinfante conventions and discuss a difference between them, which is reminiscent of a classical example of Feynman's angular momentum paradox. We point out its possible relevance to early-time dynamics in the nucleus-nucleus collisions, resulting in excess by the electromagnetic angular momentum. PrologueSome time ago we, Fukushima and Pu, together with our bright colleague, Zebin Qiu, published a paper [1] on a relativistic extension of the Barnett effect [2] in the context of chiral materials. Our results are beautiful and robust, we believe, but at the same time, we had to overcome many conceptual confusions. We are

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Feynman’s disk paradox

Abstract: A paradox involving the apparent violation of angular momentum conservation is discussed. Electromagnetic induction is used to impart angular momentum to a disk of charges. The paradox is resolved by finding the origin of the angular momentum.

Cited by 18 publications

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Self-torque and angular momentum balance for a spinning charged sphere

Self-torque and angular momentum balance for a spinning charged sphere

Introducing electromagnetic field momentum

Relativistic decomposition of the orbital and the spin angular momentum in chiral physics and Feynman's angular momentum paradox

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