# Divergence

• Feb 19th 2007, 08:50 AM
Divergence
Hi I have problem finding the solution for this problem:

Find the divergence of the vector function A=ˆρ ρ
transform this vector function into rectangular coordinates and find the
divergence using rectangular coordinates calculation.

I know that I need to find 2 since I have computed it in cylindar coordinates.
But I don't succeed to do it in rectangular coordinates.
I replace ρ by sqrt(x^2+y^2+z^2) (where in this case z=0)and
the unit vector ˆρ by ˆx*cos(phi)+ ˆy*sin(phi)

N.B: In bold this is the unit vector.
thank you.
B
• Feb 19th 2007, 08:56 AM
topsquark
Quote:

Hi I have problem finding the solution for this problem:

Find the divergence of the vector function A=ˆρ ρ
transform this vector function into rectangular coordinates and find the
divergence using rectangular coordinates calculation.

I know that I need to find 2 since I have computed it in cylindar coordinates.
But I don't succeed to do it in rectangular coordinates.
I replace ρ by sqrt(x^2+y^2+z^2) (where in this case z=0)and
the unit vector ˆρ by ˆx*cos(phi)+ ˆy*sin(phi)

N.B: In bold this is the unit vector.
thank you.
B

In the Cartesian case the formula for the divergence is simple. Just take
^x(d/dx) + ^y(d/dy)
(Since z = 0 is constant we may omit the ^z(d/dx) term.)

-Dan