- #1
UndeniablyRex
- 12
- 0
I know how to calculate the divergence and curl of a vector field. What I am lacking is any intuition on what these values mean.
example:
V= {x, y, z}
∇.V = 3
∇xV = {0,0,0}
F={-y, x, 0}
∇.F = 0
∇xF = {0,0,2}
G={0, 3y, 0}
∇.G = 3
I understand that that the divergence is a measure of how much the vector field "spreads out" and the curl measures the circulation, but what does it mean to have a divergence of 3? or a curl vector of {0,0,2}
The last example is merely because it has the same divergence as the first; the graphs look very different(the second doesn't even seem to "diverge"), yet have the same divergence.
Thank you for any help.
example:
V= {x, y, z}
∇.V = 3
∇xV = {0,0,0}
F={-y, x, 0}
∇.F = 0
∇xF = {0,0,2}
G={0, 3y, 0}
∇.G = 3
I understand that that the divergence is a measure of how much the vector field "spreads out" and the curl measures the circulation, but what does it mean to have a divergence of 3? or a curl vector of {0,0,2}
The last example is merely because it has the same divergence as the first; the graphs look very different(the second doesn't even seem to "diverge"), yet have the same divergence.
Thank you for any help.