The two-capacitor problem with radiation
Timothy B.
Boykin, Dennis Hite, and Nagendra Singh
Department of Electrical and Computer Engineering, The University of Alabama in Huntsville, Huntsville,
Alabama 35899
Received 12 June 2001; accepted 8 November 2001
We discuss the two-capacitor problem found in many introductory physics texts...
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The two-capacitor problem with radiation Timothy B. Boykin, Dennis Hite, and Nagendra Singh Department of Electrical and Computer Engineering, The University of Alabama in Huntsville, Huntsville, Alabama 35899 Received 12 June 2001; accepted 8 November 2001 We discuss the two-capacitor problem found in many introductory physics texts in which there appears to be missing energy in an ideal, zero-resistance circuit, following the sudden charging of one capacitor from another. The paradox of this missing energy is traditionally ascribed to finite-resistance wires, the initial assumption of an ideal circuit and the rapid nature of the charging notwithstanding. By treating radiative effects in the simplest approximation, we show that the paradox is really nothing more than an inappropriately applied lumped-parameter model. In particular, we show that in the zero-resistance circuit, radiation fully accounts for all of the energy lost. To explore radiative effects in more realistic circui
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From kirchhoff
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I potenziali elettrico e magnetico
Occorre distinguere, preliminarmente, fra il corso stazionario e quello non stazionario.
a) Caso stazionario
Nel caso stazionario, tutte le derivate temporali presenti nelle equazioni di Maxwell si annullano.
Dunque, la prima equazione di Maxwell in forma differenziale diventa:
0=×∇ E
Oppure,...
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I potenziali elettrico e magnetico Occorre distinguere, preliminarmente, fra il corso stazionario e quello non stazionario. a) Caso stazionario Nel caso stazionario, tutte le derivate temporali presenti nelle equazioni di Maxwell si annullano. Dunque, la prima equazione di Maxwell in forma differenziale diventa: 0=×∇ E Oppure, considerando la corrispondente equazione in forma integrale, si ha: 0d =⋅∫ l r E Quindi in questo caso E è un campo vettoriale conservativo, e può essere espresso come gradiente di un opportuno campo scalare φ: elettricoscalarePotenzialeΦΦ−∇=E La ragione del segno – davanti al gradiente è di carattere storico, si tratta di una convenzione adottata in elettromagnetismo che non altera la sostanza del discorso. Dati 2 punti P e Q dello spazio, si definisce tensione fra i punti Q e la grandezza [ ] PQQP P Q -VV(P)-Q)(d ==ΦΦ=⋅ ∆ ∫ l r E Naturalmente, la tensione dipende solo dai punti P e Q e non dal percorso sul quale viene calcolato l’integrale, essendo E conserv
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From kirchhoff
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A Capacitor Paradox
Kirk T.
McDonald
Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544
(July 10, 2002)
1 Problem
Two capacitors of equal capacitance C are connected in parallel by zero-resistance wires and
a switch, as shown in the lefthand figure below.
Initially the switch is open, one capacitor
is charged to...
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A Capacitor Paradox Kirk T. McDonald Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (July 10, 2002) 1 Problem Two capacitors of equal capacitance C are connected in parallel by zero-resistance wires and a switch, as shown in the lefthand figure below. Initially the switch is open, one capacitor is charged to voltage V0 and the other is uncharged. At time t = 0 the switch is closed. If there were no damping mechanism, the circuit would then oscillate forever, at a frequency dependent on the self inductance L and the capacitance C. However, even in a circuit with zero Ohmic resistance, damping occurs due to the radiation of the oscillating charges, and eventually a static charge distribution results. 1. How much energy is stored in the system before and (a long time) after the switch is closed? The paradox is that these two energies are not equal. 2. Verify that the “missing” stored energy has been radiated away by the transient current after the switch was
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From kirchhoff
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NOTES AND DISCUSSIONS
Ideal capacitor circuits and energy conservation
K.
Mita and M.
Boufaida
Department of Physics, St.
Mary’s College of Maryland, St.
Mary’s City, Maryland 20686
Received 20 July 1998; accepted 8 December 1998
In some introductory physics textbooks, authors point out
that there is missing energy in the...
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NOTES AND DISCUSSIONS Ideal capacitor circuits and energy conservation K. Mita and M. Boufaida Department of Physics, St. Mary’s College of Maryland, St. Mary’s City, Maryland 20686 Received 20 July 1998; accepted 8 December 1998 In some introductory physics textbooks, authors point out that there is missing energy in the charging process of the capacitor circuit in Fig. 1 a . 1 In some other textbooks, they present a problem in which a portion of the electric charge is transferred from a fully charged capacitor to an empty one, as shown in Fig. 1 b . 2 In either case, half the energy of the circuit is missing in the final state after the switch S is thrown. The usual way to circumvent this difficulty is to introduce a small amount of resistance in the connecting wires to explain that the missing energy is dissipated as Joule heating. While this argument appears correct, it leaves us feeling unsettled. We wonder why is it that the energy is missing in the circuits in Fig. 1 a o
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From kirchhoff
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INDICE
Introduzione.
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From kirchhoff
HB214/D
Rev.
2, Nov-2001
Rectifier Applications
Handbook
From kirchhoff
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This is a digital copy of a book that was preserved for generations on library shelves before it was carefully scanned by Google as part of a project
to make the world’s books discoverable online.
It has survived long enough for the copyright to expire and the book to enter the public domain.
A public domain book is one that was...
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This is a digital copy of a book that was preserved for generations on library shelves before it was carefully scanned by Google as part of a project to make the world’s books discoverable online. It has survived long enough for the copyright to expire and the book to enter the public domain. A public domain book is one that was never subject to copyright or whose legal copyright term has expired. Whether a book is in the public domain may vary country to country. Public domain books are our gateways to the past, representing a wealth of history, culture and knowledge that’s often difficult to discover. Marks, notations and other marginalia present in the original volume will appear in this file - a reminder of this book’s long journey from the publisher to a library and finally to you. Usage guidelines Google is proud to partner with libraries to digitize public domain materials and make them widely accessible. Public domain books belong to the public and we are merely their custo
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Italy
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