aaronfue said:Homework Statement
Calculate the curl F:
F(x,y,z) = cos(x)i + sin(y)j + exyk at point (1,1,1)
Homework Equations
The Attempt at a Solution
After calculating ∇×F, my answer was:
curl F = 2.72i + 2.72j + 0k
I'd appreciate a confirmation of my answer.
Dick said:No answer is possible until you say at what point you are evaluating the curl. Come on.
aaronfue said:Sorry. Point noted in question.
Dick said:Yeah, my over sight. But I'm getting [e,-e,0]. Can you check that again?
aaronfue said:Yeah, my answer should be [e,-e,0]. I forgot to put a negative on the second rather than a positive.
Answer should be:
curl F = 2.72i - 2.72j + 0k
or
curl F = ei - ej + 0k
Dick said:Then I'll confirm that.
The formula for calculating the curl of a vector field at a specific point is given by ∇ x F = ( ∂F₃/∂y - ∂F₂/∂z, ∂F₁/∂z - ∂F₃/∂x, ∂F₂/∂x - ∂F₁/∂y ) where F is the vector field and ∇ is the del operator.
To confirm the answer for the curl of a vector field at a specific point, you can use the formula mentioned in the previous question and plug in the values of the given vector field at the specified point. If the resulting values match the calculated curl, then the answer is confirmed.
The curl of a vector field represents the tendency of the vector field to rotate or circulate around a specific point. It is a measure of the rotational or circular motion of the vector field.
The curl of a vector field and its divergence are related through the divergence theorem, which states that the divergence of a vector field is equal to the flux of its curl. In other words, the curl of a vector field represents the rotational components while the divergence represents the expanding or contracting components of the vector field.
Yes, the curl of a vector field can be negative. The sign of the curl depends on the direction of the rotation of the vector field. If the rotation is clockwise, the curl will be negative and if it is counterclockwise, the curl will be positive.