What is the curl of F for given vector fields?

  • Thread starter hallnate
  • Start date
  • Tags
    Curl
In summary, the first function has a wrong jth component and the second function has a wrong ith component.
  • #1
2
0

Homework Statement


1.F=(x-8z)i+(x+9y+z)j+(x-8y)k find the curl of F

Homework Equations


curl of F= del X F

The Attempt at a Solution


1. First I took the partial with respect to y of (x-8y) and subtracted the partial with respect to z of (x+9y+z). From this I got (-8-1) Then I took the partial with respect to x of (x-8y) and subtracted the partial with respect to z of (x-8z), getting (1+8). I then took the partial with respect to x of (x+9y+z) and subtracted the partial with respect to y of (x-8z), getting (1-0). So I took (-8-1)-(1+8)+(1-0) and got an answer of 1, but this was wrong.

Homework Statement


2.F=(7e^x)i-(14e^y)j+(7e^z)k find the curl of F

Homework Equations


curl of F= del X F

The Attempt at a Solution


2. For this, since I was always going to be taking the partial with respect to a variable that was not in that part of the function, everything would be zero. Ex: partial with respect to x of -14e^y should be zero I believe
 
Physics news on Phys.org
  • #2
For the curl of the first function I think that in finding the jth component of curlF you have to take the partial wrt z of (x-8z) and subtract from this the partial wrt x of (x-8y) but you did the reverse.

Note also that curl F is a vector and so it must remain as i(...) +j(...) +k(...).
 
Last edited:
  • #3
Yes the curl of the second function F gives the zero vector.
 
  • #4
grzz said:
Yes the curl of the second function F gives the zero vector.

I thought so. I entered this in and it was wrong. I'll just try emailing my professor.
 

What is the definition of "curl" in physics?

Curl is a mathematical operation that describes the rotation or circulation of a vector field. It is represented by the symbol ∇ × F and is used to measure the amount of circulation or rotation at a given point in space.

How do you find the curl of a vector field?

The curl of a vector field can be found by taking the partial derivatives of each component of the vector field with respect to each coordinate variable, and then taking the cross product of those derivatives. This can be represented mathematically as ∇ × F = (∂Fz/∂y - ∂Fy/∂z)i + (∂Fx/∂z - ∂Fz/∂x)j + (∂Fy/∂x - ∂Fx/∂y)k.

What is the physical interpretation of the curl of a vector field?

The curl of a vector field represents the amount of rotation or circulation of the vector field at a given point in space. It can also be thought of as a measure of the local angular velocity of the vector field.

How does the curl of a vector field relate to its divergence?

In three-dimensional space, the curl of a vector field is related to its divergence through the Maxwell's equations of electromagnetism. Specifically, the divergence of a vector field represents the net flux of the field out of a closed surface, while the curl represents the circulation of the field around a closed loop within the surface. This relationship is known as the divergence theorem.

What are some practical applications of finding the curl of a vector field?

The curl of a vector field has many practical applications, particularly in physics and engineering. It is used in fluid mechanics to understand the flow of fluids, in electromagnetism to describe electromagnetic fields, and in mechanics to analyze the rotation of rigid bodies. It is also used in computer graphics to create realistic simulations of fluid flow and other physical phenomena.

Suggested for: What is the curl of F for given vector fields?

Back
Top