- #1

Brad Barker

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**griffiths electrostatics problem**

if you have the text on you, I'm looking at question 2.46 (in the third edition).

i am given

[tex]

V(\mathbf{r}) = A\exp (-\lambda r)/r

[/tex]

i found that

[tex]

\mathbf{E} (\mathbf{r}) = A\exp (-\lambda r)(\lambda /r + 1/r^2) \hat{r}

[/tex]

the solution for [tex]\rho[/tex] given in the text is

[tex]

\rho = \epsilon _0 A [4\pi \delta^3 (\mathbf{r}) - \lambda^2 \exp (-\lambda r)/r]

[/tex]

however, in my solution, i got that exponential funtcion multiplying both terms in the answer.

i don't think i made a mistake in my steps, either. :/

i used the following properties:

[tex]

\nabla \cdot (f\mathbf{A}) = f(\nabla \cdot \mathbf{A}) + \mathbf{A} \cdot (\nabla f)

[/tex]

and

[tex]

\nabla \cdot (\mathbf{A} + \mathbf{B}) = \nabla \cdot \mathbf{A} + \nabla \cdot \mathbf{B}

[/tex]

from that first property, the first term on the right hand side seems to me to make it pretty clear that the exponential function should be in both terms in the answer. :/

thank you.

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