“…Gravitational interactions were described in terms of forces obeying an inverse square law. Laplace and others had developed the notion of a field as force per unit mass, but employed it purely as a mathematical tool [1].…”
Section: Epistemological Development Of the Classical Theory Of Tmentioning
confidence: 99%
“…The noncentral character of the magnetic force discovered by Oersted and Ampère was one of the phenomena that spurred Faraday on to imagine a role for the surroundings in which the interaction took place. Further new experimental facts such as the finding that containers with air pressure maintained the charges better on a conductor; the influence of arranging different materials in Voltaic piles; the discovery of electro-optic and magneto-optic and electrochemical phenomena all lent credence to the notion that the space between charged bodies ("the medium") must be given a prominent role [1]. A second driving force for the development of field theory came from the search for underlying unity of natural forces, culminating in the law of the conservation of energy formulated in 1840 [15].…”
Section: Epistemological Development Of the Classical Theory Of Tmentioning
confidence: 99%
“…The above discussion of the historical development provides important hints as to where students may have problems in the construction of concepts and theories. We have distinguished five key characteristics of the electrostatic and magnetostatic field that we deem relevant and attainable at the introductory university physics level (selected from characteristics identified by [1,14,15]) KC1. The electrostatic field is produced by charges and the magnetic field is produced by moving charges (currents or magnets).…”
Section: Epistemological Development Of the Classical Theory Of Tmentioning
confidence: 99%
“…It is more abstract than the Newtonian theory that is based on forces only, but has greater explanatory power (see, e.g., Ref. [1]).…”
In this work, we explore how undergraduate students use classical field theory when describing physical phenomena in the context of introductory electromagnetism. We have extracted five key characteristics of the electric and magnetic field from a historical analysis of the topic. These characteristics informed the creation of a questionnaire comprising six free-response conceptual questions. The questionnaire instrument was administered to undergraduate students in three European countries. Phenomenographical analysis of the students' responses shows that many undergraduates do not have a coherent idea of field theory. We conclude that, rather than focusing on teaching rules with which to calculate, more attention should be paid to the specific characteristics of field theory and the difference between fields and forces, with particular emphasis on the conceptual interpretation of the interaction process.
“…Gravitational interactions were described in terms of forces obeying an inverse square law. Laplace and others had developed the notion of a field as force per unit mass, but employed it purely as a mathematical tool [1].…”
Section: Epistemological Development Of the Classical Theory Of Tmentioning
confidence: 99%
“…The noncentral character of the magnetic force discovered by Oersted and Ampère was one of the phenomena that spurred Faraday on to imagine a role for the surroundings in which the interaction took place. Further new experimental facts such as the finding that containers with air pressure maintained the charges better on a conductor; the influence of arranging different materials in Voltaic piles; the discovery of electro-optic and magneto-optic and electrochemical phenomena all lent credence to the notion that the space between charged bodies ("the medium") must be given a prominent role [1]. A second driving force for the development of field theory came from the search for underlying unity of natural forces, culminating in the law of the conservation of energy formulated in 1840 [15].…”
Section: Epistemological Development Of the Classical Theory Of Tmentioning
confidence: 99%
“…The above discussion of the historical development provides important hints as to where students may have problems in the construction of concepts and theories. We have distinguished five key characteristics of the electrostatic and magnetostatic field that we deem relevant and attainable at the introductory university physics level (selected from characteristics identified by [1,14,15]) KC1. The electrostatic field is produced by charges and the magnetic field is produced by moving charges (currents or magnets).…”
Section: Epistemological Development Of the Classical Theory Of Tmentioning
confidence: 99%
“…It is more abstract than the Newtonian theory that is based on forces only, but has greater explanatory power (see, e.g., Ref. [1]).…”
In this work, we explore how undergraduate students use classical field theory when describing physical phenomena in the context of introductory electromagnetism. We have extracted five key characteristics of the electric and magnetic field from a historical analysis of the topic. These characteristics informed the creation of a questionnaire comprising six free-response conceptual questions. The questionnaire instrument was administered to undergraduate students in three European countries. Phenomenographical analysis of the students' responses shows that many undergraduates do not have a coherent idea of field theory. We conclude that, rather than focusing on teaching rules with which to calculate, more attention should be paid to the specific characteristics of field theory and the difference between fields and forces, with particular emphasis on the conceptual interpretation of the interaction process.
“…It has been shown that all disc automorphisms of a nontrivial one-parameter group family of disc automorphisms share the same fixed points, cf. [5]. Thus, we consider the following three cases:…”
In this paper we describe the surjective linear isometries on a vector valued little Bloch space with range space a strictly convex and smooth complex Banach space. We also describe the hermitian operators and the generalized bi-circular projections supported by these spaces.
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