Confussion about Del operator for field point vs source point.

[yungman]

I electrodynamics, I've seen [itex]\nabla ' [/itex] and [itex]\nabla [/itex] where first is spatial derivative respect to source point and later spatial derivative respect to field point.

I am confuse. According to multi-variables calculus, the [itex] \nabla[/itex] operator is spatial derivative of either a scalar or a vector field. Both of which are point form...which is absolutely spatial dependent only. I don't see what is the meaning respect to source or field points.

For example:

[itex]\nabla V [/itex] is the gradient of a scalar function V, and it has a different value at each individual point specified. So is [itex]\nabla \cdot \vec E[/itex] which is the divergence at a point in the space. These are regardless of whether it is a field or a source point.

I am confused. Please explain to me.

Thanks

Alan

 

[Meir Achuz]

The integrand in the integral for phi is a function f(r,r') of two variables, r and r'.
Del acts on r, and Del' acts on r'.

 

[yungman]

Thanks

Alan