Confussion about Del operator for field point vs source point.

In summary, the \nabla operator in electrodynamics is a spatial derivative of either a scalar or a vector field. It represents the change in the field at a specific point. This can be seen in examples such as \nabla V, the gradient of a scalar function, and \nabla \cdot \vec E, the divergence at a point in space. The operator acts on both the source point and the field point, represented by r and r' respectively.
  • #1
yungman
5,726
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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
 
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  • #2
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'.
 
  • #3
Thanks

Alan
 

Related to Confussion about Del operator for field point vs source point.

1. What is the Del operator used for in science?

The Del operator, represented by the symbol ∇, is used in mathematics and science to represent the gradient, divergence, and curl of a vector field. It is a vector operator that is commonly used in fields such as physics, engineering, and fluid mechanics.

2. What is the difference between the Del operator for field point and source point?

The Del operator for field point is used to calculate the values of a vector field at a particular point in space, while the Del operator for source point is used to calculate the values of a vector field at the location of its source. The two operators have different mathematical formulas and are used for different purposes.

3. How is the Del operator applied in vector calculus?

In vector calculus, the Del operator is applied to a function or a vector field to calculate its gradient, divergence, or curl. It is typically used in conjunction with other operators, such as the dot and cross product, to solve complex problems in mathematics and science.

4. Can the Del operator be used in any coordinate system?

Yes, the Del operator can be used in any coordinate system, including Cartesian, cylindrical, and spherical coordinates. However, the specific formulas for the operator may differ slightly depending on the coordinate system being used.

5. What are some practical applications of the Del operator?

The Del operator has many practical applications in science and engineering. It is used in fluid dynamics to model the flow of fluids, in electromagnetism to calculate the electric and magnetic fields, and in mechanics to analyze forces and motion. It is also used in fields such as computer graphics, image processing, and signal processing.

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