- #1
nuclear_dog
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In Griffiths, for deriving the bound charges for a given polarization P , the formula used is the general formula for dipoles .i.e ( equation 4.9)
{Here the potential at r is calculated due to the dipole at r' )
V(r) = ∫[itex]\frac{x.P(r')}{X^2}[/itex]d[itex]\tau'[/itex]
Here X = r - r' , and x = unit vector in the direction of X
Then it is written that [itex]\frac{x}{X^2}[/itex] = [itex]\nabla'[/itex](1/X).
since X = (r-r') , and ∇' = (∂/∂r')[itex]\widehat{r'}[/itex] ...
Shouldn't ∇'(1/X) be (1/X^2)[itex]\widehat{r'}[/itex] ?
{Here the potential at r is calculated due to the dipole at r' )
V(r) = ∫[itex]\frac{x.P(r')}{X^2}[/itex]d[itex]\tau'[/itex]
Here X = r - r' , and x = unit vector in the direction of X
Then it is written that [itex]\frac{x}{X^2}[/itex] = [itex]\nabla'[/itex](1/X).
since X = (r-r') , and ∇' = (∂/∂r')[itex]\widehat{r'}[/itex] ...
Shouldn't ∇'(1/X) be (1/X^2)[itex]\widehat{r'}[/itex] ?
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