- #1
yungman
- 5,718
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In page 555, Appendix B of Intro to electrodynamics by D Griffiths:
[tex]\nabla\cdot \vec F=-\nabla^2U=-\frac{1}{4\pi}\int D\nabla^2\left(\frac{1}{\vec{\vartheta}}\right)d\tau'=\int D(\vec r')\delta^3(\vec r-\vec r')d\tau'=D(\vec r) [/tex]
where ##\;\vec{\vartheta}=\vec r-\vec r'##.
Is it supposed to be equal to ##D(\vec r')## as equation (1.98) in page 50 stated ##\int f(\vec r)\delta(\vec r-\vec a)d\tau'=f(\vec a)##?
Thanks
[tex]\nabla\cdot \vec F=-\nabla^2U=-\frac{1}{4\pi}\int D\nabla^2\left(\frac{1}{\vec{\vartheta}}\right)d\tau'=\int D(\vec r')\delta^3(\vec r-\vec r')d\tau'=D(\vec r) [/tex]
where ##\;\vec{\vartheta}=\vec r-\vec r'##.
Is it supposed to be equal to ##D(\vec r')## as equation (1.98) in page 50 stated ##\int f(\vec r)\delta(\vec r-\vec a)d\tau'=f(\vec a)##?
Thanks