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Thanks.

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- Thread starter eok20
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- #1

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Thanks.

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Claude Bile

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The problem lies in the fact that you are using a point charge. Discontinuities such as these are commonly represented by the Dirac delta function that is defined as follows (for 3 dimensions).

[tex] \int_{V} \delta(r) d\tau = 1 [/tex]

where V is any volume that contains the origin. Also;

[tex] \delta(r) = 0 [/tex] for r not equal to 0

[tex] \delta(r) = \infty [/tex] for r equal to 0

The problem is that when you calculate the divergence, it does not include the origin (since at the origin you are effectively dividing by zero). When the charged sphere has a finite radius, this is not a problem, because the contribution from the origin is infinitesimally small. In the case of the point charge however, the*entire* contribution is coming from the origin, hence the original error.

To fix this, you need to include the Dirac delta function when you calculate the volume integral.

Claude.

[tex] \int_{V} \delta(r) d\tau = 1 [/tex]

where V is any volume that contains the origin. Also;

[tex] \delta(r) = 0 [/tex] for r not equal to 0

[tex] \delta(r) = \infty [/tex] for r equal to 0

The problem is that when you calculate the divergence, it does not include the origin (since at the origin you are effectively dividing by zero). When the charged sphere has a finite radius, this is not a problem, because the contribution from the origin is infinitesimally small. In the case of the point charge however, the

To fix this, you need to include the Dirac delta function when you calculate the volume integral.

Claude.

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