What is the definition of vector operator "delta" and I want to have a larger view about divergence theorem.

Question

please help me yahoo members...... it is covered by the topic electromagnetics

Answer 1

The vector operator "delta" which is like a upsidedown triangle is defined as the partial dervivative of x,y,z respectively in vector form. It is used as a dot product of the given vector function in a triple integral.

In multivariable calculus, the Gaussian Divergence Theorm was used by James Clark Maxwell in his equations to describe eletromagnetism.

Answer 2

The "delta" vector operator is actually the gradient operator, and the divergence of a vector field is expressed by the dot product of the gradient operator with the function defining the vector field. That is:

div F = V * F

where V is the delta or gradient operator, * is the dot product, and F the function of the vector field. The divergence theorem conceptually is pretty straightforward: If I want to compute the net flow across the boundary of any closed surface, I add up the sources and sinks contained inside the closed boundary. That is, the sum of all sources minus the sum of all sinks gives the net flow out of a region. Pretty obvious, huh?

Answer 3

delta( or del ) is vector differential operator .delta=id/dx +jd/dy +kd/dz.
all these are partial derivatives.

According to divergence theorem,
"The integral of the divergence of a vector field over a volume V is equal to the surface integral of the normal component of the vector over the surface bounding the volume"

volume integral(divF dv)= surface integral(F.normal unit vector.ds).

Answer 4

If f=f(x,y,z), then del f=idf/dx+jdf/dy+kdf/dz. Where d=partial derivative, i,j,k are unit vectors in the x,y,z directions respectively.
Now del a=grad a
del dot A=div A
del Cross A=curl A, where a is a scalar and A is a vector.

Answer 5

I believe that the delta is the gradient.