We show that a form for the second partial derivative of proposed by Frahm and subsequently used by other workers applies only when averaged over smooth functions. We use dyadic notation to derive a more general form without that restriction.
REFERENCES
1.
Charles P.
Frahm
, “Some novel delta-function identities
,” Am. J. Phys.
51
(9
), 826
–829
(1983
).2.
Jeffrey M.
Bowen
, “Delta function terms arising from classical point-source fields
,” Am. J. Phys.
62
, 511
–515
(1994
).3.
Ricardo
Estrada
and Ram P.
Kanwal
, “The appearance of nonclassical terms in the analysis of point-source fields
,” Am. J. Phys.
63
, 278
(1995
).4.
P. T.
Leung
and G. J.
Ni
, “On the singularities of the electrostatic and magnetostatic dipole fields
,” Eur. J. Phys.
27
, N1
–N3
(2006
).5.
6.
A brief review of dyadic notation is given in
J.
Franklin
, Classical Electromagnetism
(Pearson Addison-Wesley
, San Francisco
, 2005
), Sec. 2.4.7.
Reference 6, p.
52
.8.
Reference 6, p.
211
.© 2010 American Association of Physics Teachers.
2010
American Association of Physics Teachers
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