# Vector field notation help

1. Feb 12, 2007

### JaysFan31

Just a quick question about notation.

I was given the vector field

F = r + grad(1/bar(r)) where r= (x)i+(y)j+(z)k.
grad is just written as the upside down delta (gradient) and the bar I wrote in the above equation looks like an absolute value around just the r (although I don't know if it is absolute value). Basically I want to find the gradient of (1/bar(r)).

What would be a simplification of this vector field so that I can solve the rest of the problem?

I want to find its flux across the surface of a sphere.

I think F would be ((x^3)-1)/x^2+((y^3)-1)/y^2+((z^3-1)/z^2, but I'm not sure.

2. Feb 12, 2007

### neutrino

$$|\vec{r}|$$ is the modulus, or magnitude, of vector $$\vec{r}$$.

3. Feb 12, 2007

### HallsofIvy

Staff Emeritus
If $\vec{r}= x\vec{i}+ y\vec{j}+ z\vec{k}$ then
$$\frac{1}{||\vec{r}||}= \frac{1}{\sqrt{x^2+y^2+ z^2}}= (x^2+y^2+ z^2)^{-\frac{1}{2}}$$
What is the gradient of that function?

4. Feb 12, 2007

### JaysFan31

How can you take the gradient of the function if it doesn't have i, j, and k?

Is it 0?

5. Feb 13, 2007

### cepheid

Staff Emeritus
A better question would be, how could you take the grad of the function if it *did* have i, j, and k? Remember, the gradient acts on a scalar.

6. Feb 13, 2007

### HallsofIvy

Staff Emeritus
Well, you would first have to know what "gradient" actually means!

Given a function f(x,y,z), how would YOU define
$\nabla f$?