Abstract

The commented paper [J. Opt. Soc. Am. A 25, 543 (2008] denies the truth of a standard general formula of electrodynamics [Eq. (6.52) of Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999)]). The motivation for challenging orthodoxy is that the formula directly disproves the repeated claim of the commented authors that electromagnetic radiation, under some circumstances, can have unusually long range. The formula they challenge is for the magnetic field: B=Integral over all space of (μ04π)[Curlj]Range. Instead they advocate a (correct) formula for the vector potential: A=Integral over all space of (μ04π)[j]Range. However, as one might suppose, the former equation follows as a purely mathematical consequence of taking the curl of the latter equation. This is straightforward to make rigorous in the particular circumstances in question (confined smooth current density j). Therefore by their own formula, the standard one of electrodynamics is confirmed, and the disproof of their long range claim stands.

© 2009 Optical Society of America

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  1. H. Ardavan, A. Ardavan, J. Singleton, J. Fasel, and A. Schmidt, “Fundamental role of the retarded potential in the electrodynamics of superluminal sources,” J. Opt. Soc. Am. A 25, 543-557 (2008).
    [CrossRef]
  2. J. D. Jackson, Classical Electrodynamics, 3rd. ed. (Wiley, 1999).
  3. J. H. Hannay, “Morphology of the nonspherically decaying radiation beam generated by a rotating superluminal source: comment,” J. Opt. Soc. Am. A 25, 2165-2166 (2008).
    [CrossRef]
  4. J. H. Hannay “Spectral and polarization characteristics of the nonspherically decaying radiation generated by polarization currents with superluminally rotating distribution patterns: comment,” J. Opt. Soc. Am. A 23, 1530-1534 (2006).
    [CrossRef]
  5. J. H. Hannay “Comment on 'Method of handling the divergences in the radiation theory of sources that move faster than their waves,'” J. Math. Phys. 42, 3973-3974 (2001).
    [CrossRef]
  6. J. H. Hannay, “Comment II on 'Generation of focused, nonspherically decaying pulses of electromagnetic radiation,” Phys. Rev. E 62, 3008-3009 (2000).
    [CrossRef]
  7. J. H. Hannay, “Bounds on fields from fast rotating sources, and others,” Proc. R. Soc. London, Ser. A 452, 2351-2354 (1996). (The factor half in Eqs. 1.1, 1.5, 1.6 should be replaced by two instead, the rest of the equations being unaffected).
    [CrossRef]
  8. H. Ardavan, A. Ardavan, J. Singleton, J. Fasel, and A. Schmidt, “Morphology of the nonspherically decaying radiation beam generated by a rotating superluminal source,” J. Opt. Soc. Am. A 25, 2443-2456 (2007).
    [CrossRef]
  9. H. Ardavan, A. Ardavan, and J. Singleton, “Spectral and polarization characteristics of the nonspherically decaying radiation generated by polarization currents with superluminally rotating distribution patterns,” J. Opt. Soc. Am. A 21, 858-872 (2004).
    [CrossRef]
  10. H. Ardavan, “Method of handling the divergences in the radiation theory of sources that move faster than their waves,” J. Math. Phys. 40, 4331-4336 (1999).
    [CrossRef]
  11. H. Ardavan, “Generation of focused, nonspherically decaying pulses of electromagnetic radiation,” Phys. Rev. E 58, 6659-6684 (1998).
    [CrossRef]
  12. H. Ardavan, “The mechanism of radiation in pulsars,” Mon. Not. R. Astron. Soc. 268, 361-392 (1994).
  13. H. Ardavan, “The near-field singularity predicted by the spiral Green's function in acoustics and electrodynamics,” Proc. R. Soc. London, Ser. A 433, 451-459 (1991).
    [CrossRef]
  14. H. Ardavan, A. Ardavan, J. Singleton, J. Fasel, and A. Schmidt, “Morphology of the nonspherically decaying radiation beam generated by a rotating superluminal source: reply to comment,” J. Opt. Soc. Am. A 25, 2167-2169 (2008).
    [CrossRef]
  15. H. Ardavan, A. Ardavan, and J. Singleton, “Spectral and polarization characteristics of the nonspherically decaying radiation generated by polarization currents with superluminally rotating distribution patterns: reply to comment,” J. Opt. Soc. Am. A 23, 1535-1539 (2006).
    [CrossRef]

2008 (3)

2007 (1)

H. Ardavan, A. Ardavan, J. Singleton, J. Fasel, and A. Schmidt, “Morphology of the nonspherically decaying radiation beam generated by a rotating superluminal source,” J. Opt. Soc. Am. A 25, 2443-2456 (2007).
[CrossRef]

2006 (2)

2004 (1)

2001 (1)

J. H. Hannay “Comment on 'Method of handling the divergences in the radiation theory of sources that move faster than their waves,'” J. Math. Phys. 42, 3973-3974 (2001).
[CrossRef]

2000 (1)

J. H. Hannay, “Comment II on 'Generation of focused, nonspherically decaying pulses of electromagnetic radiation,” Phys. Rev. E 62, 3008-3009 (2000).
[CrossRef]

1999 (1)

H. Ardavan, “Method of handling the divergences in the radiation theory of sources that move faster than their waves,” J. Math. Phys. 40, 4331-4336 (1999).
[CrossRef]

1998 (1)

H. Ardavan, “Generation of focused, nonspherically decaying pulses of electromagnetic radiation,” Phys. Rev. E 58, 6659-6684 (1998).
[CrossRef]

1996 (1)

J. H. Hannay, “Bounds on fields from fast rotating sources, and others,” Proc. R. Soc. London, Ser. A 452, 2351-2354 (1996). (The factor half in Eqs. 1.1, 1.5, 1.6 should be replaced by two instead, the rest of the equations being unaffected).
[CrossRef]

1994 (1)

H. Ardavan, “The mechanism of radiation in pulsars,” Mon. Not. R. Astron. Soc. 268, 361-392 (1994).

1991 (1)

H. Ardavan, “The near-field singularity predicted by the spiral Green's function in acoustics and electrodynamics,” Proc. R. Soc. London, Ser. A 433, 451-459 (1991).
[CrossRef]

Ardavan, A.

Ardavan, H.

H. Ardavan, A. Ardavan, J. Singleton, J. Fasel, and A. Schmidt, “Fundamental role of the retarded potential in the electrodynamics of superluminal sources,” J. Opt. Soc. Am. A 25, 543-557 (2008).
[CrossRef]

H. Ardavan, A. Ardavan, J. Singleton, J. Fasel, and A. Schmidt, “Morphology of the nonspherically decaying radiation beam generated by a rotating superluminal source: reply to comment,” J. Opt. Soc. Am. A 25, 2167-2169 (2008).
[CrossRef]

H. Ardavan, A. Ardavan, J. Singleton, J. Fasel, and A. Schmidt, “Morphology of the nonspherically decaying radiation beam generated by a rotating superluminal source,” J. Opt. Soc. Am. A 25, 2443-2456 (2007).
[CrossRef]

H. Ardavan, A. Ardavan, and J. Singleton, “Spectral and polarization characteristics of the nonspherically decaying radiation generated by polarization currents with superluminally rotating distribution patterns: reply to comment,” J. Opt. Soc. Am. A 23, 1535-1539 (2006).
[CrossRef]

H. Ardavan, A. Ardavan, and J. Singleton, “Spectral and polarization characteristics of the nonspherically decaying radiation generated by polarization currents with superluminally rotating distribution patterns,” J. Opt. Soc. Am. A 21, 858-872 (2004).
[CrossRef]

H. Ardavan, “Method of handling the divergences in the radiation theory of sources that move faster than their waves,” J. Math. Phys. 40, 4331-4336 (1999).
[CrossRef]

H. Ardavan, “Generation of focused, nonspherically decaying pulses of electromagnetic radiation,” Phys. Rev. E 58, 6659-6684 (1998).
[CrossRef]

H. Ardavan, “The mechanism of radiation in pulsars,” Mon. Not. R. Astron. Soc. 268, 361-392 (1994).

H. Ardavan, “The near-field singularity predicted by the spiral Green's function in acoustics and electrodynamics,” Proc. R. Soc. London, Ser. A 433, 451-459 (1991).
[CrossRef]

Fasel, J.

Hannay, J. H.

J. H. Hannay, “Morphology of the nonspherically decaying radiation beam generated by a rotating superluminal source: comment,” J. Opt. Soc. Am. A 25, 2165-2166 (2008).
[CrossRef]

J. H. Hannay “Spectral and polarization characteristics of the nonspherically decaying radiation generated by polarization currents with superluminally rotating distribution patterns: comment,” J. Opt. Soc. Am. A 23, 1530-1534 (2006).
[CrossRef]

J. H. Hannay “Comment on 'Method of handling the divergences in the radiation theory of sources that move faster than their waves,'” J. Math. Phys. 42, 3973-3974 (2001).
[CrossRef]

J. H. Hannay, “Comment II on 'Generation of focused, nonspherically decaying pulses of electromagnetic radiation,” Phys. Rev. E 62, 3008-3009 (2000).
[CrossRef]

J. H. Hannay, “Bounds on fields from fast rotating sources, and others,” Proc. R. Soc. London, Ser. A 452, 2351-2354 (1996). (The factor half in Eqs. 1.1, 1.5, 1.6 should be replaced by two instead, the rest of the equations being unaffected).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd. ed. (Wiley, 1999).

Schmidt, A.

Singleton, J.

J. Math. Phys. (2)

J. H. Hannay “Comment on 'Method of handling the divergences in the radiation theory of sources that move faster than their waves,'” J. Math. Phys. 42, 3973-3974 (2001).
[CrossRef]

H. Ardavan, “Method of handling the divergences in the radiation theory of sources that move faster than their waves,” J. Math. Phys. 40, 4331-4336 (1999).
[CrossRef]

J. Opt. Soc. Am. A (7)

H. Ardavan, A. Ardavan, J. Singleton, J. Fasel, and A. Schmidt, “Morphology of the nonspherically decaying radiation beam generated by a rotating superluminal source: reply to comment,” J. Opt. Soc. Am. A 25, 2167-2169 (2008).
[CrossRef]

H. Ardavan, A. Ardavan, and J. Singleton, “Spectral and polarization characteristics of the nonspherically decaying radiation generated by polarization currents with superluminally rotating distribution patterns: reply to comment,” J. Opt. Soc. Am. A 23, 1535-1539 (2006).
[CrossRef]

H. Ardavan, A. Ardavan, J. Singleton, J. Fasel, and A. Schmidt, “Morphology of the nonspherically decaying radiation beam generated by a rotating superluminal source,” J. Opt. Soc. Am. A 25, 2443-2456 (2007).
[CrossRef]

H. Ardavan, A. Ardavan, and J. Singleton, “Spectral and polarization characteristics of the nonspherically decaying radiation generated by polarization currents with superluminally rotating distribution patterns,” J. Opt. Soc. Am. A 21, 858-872 (2004).
[CrossRef]

H. Ardavan, A. Ardavan, J. Singleton, J. Fasel, and A. Schmidt, “Fundamental role of the retarded potential in the electrodynamics of superluminal sources,” J. Opt. Soc. Am. A 25, 543-557 (2008).
[CrossRef]

J. H. Hannay, “Morphology of the nonspherically decaying radiation beam generated by a rotating superluminal source: comment,” J. Opt. Soc. Am. A 25, 2165-2166 (2008).
[CrossRef]

J. H. Hannay “Spectral and polarization characteristics of the nonspherically decaying radiation generated by polarization currents with superluminally rotating distribution patterns: comment,” J. Opt. Soc. Am. A 23, 1530-1534 (2006).
[CrossRef]

Mon. Not. R. Astron. Soc. (1)

H. Ardavan, “The mechanism of radiation in pulsars,” Mon. Not. R. Astron. Soc. 268, 361-392 (1994).

Phys. Rev. E (2)

H. Ardavan, “Generation of focused, nonspherically decaying pulses of electromagnetic radiation,” Phys. Rev. E 58, 6659-6684 (1998).
[CrossRef]

J. H. Hannay, “Comment II on 'Generation of focused, nonspherically decaying pulses of electromagnetic radiation,” Phys. Rev. E 62, 3008-3009 (2000).
[CrossRef]

Proc. R. Soc. London, Ser. A (2)

J. H. Hannay, “Bounds on fields from fast rotating sources, and others,” Proc. R. Soc. London, Ser. A 452, 2351-2354 (1996). (The factor half in Eqs. 1.1, 1.5, 1.6 should be replaced by two instead, the rest of the equations being unaffected).
[CrossRef]

H. Ardavan, “The near-field singularity predicted by the spiral Green's function in acoustics and electrodynamics,” Proc. R. Soc. London, Ser. A 433, 451-459 (1991).
[CrossRef]

Other (1)

J. D. Jackson, Classical Electrodynamics, 3rd. ed. (Wiley, 1999).

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Equations (5)

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A ( r 0 , t 0 ) = μ 0 4 π t 0 j ( r , t ) | r 0 r | δ ( | r 0 r | c ( t 0 t ) ) d 3 r d t = μ 0 4 π [ j ] | r 0 r | d 3 r ,
0 A ( r 0 , t 0 ) = μ 0 4 π 0 ( 1 | r 0 r | ) [ j ] + 1 | r 0 r | 0 [ j ] d 3 r ,
= μ 0 4 π ( 1 | r 0 r | ) [ j ] 1 | r 0 r | ( [ j ] [ j ] ) d 3 r ,
= μ 0 4 π ( [ j ] | r 0 r | ) + [ j ] | r 0 r | d 3 r ,
B ( r 0 , t 0 ) = μ 0 4 π [ j ] | r 0 r | d 3 r ,

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