Cross Products: Solve For A Given B z-hat

[Nusc]

Homework Statement

B = grad(A)

Find A
If one is given B z-hat

Homework Equations

The Attempt at a Solution

What mathematical operation would I apply to solve this?

 

[neu]

Do you know what grad is?
$$B= \nabla A= \left(\frac{\partial}{\partial x}\hat{\textbf{x}} + \frac{\partial}{\partial y}\hat{\textbf{y}} + \frac{\partial}{\partial z}\hat{\textbf{z}}\right) A$$

 

[HallsofIvy]

By "one is given B z-hat" do you mean you are given only the z-component of grad A?
Then there are many solutions. For example, if we are given that the z-component of grad A, then A can be any function of x,y- as long as it has no dependence on z, the z-component of grad A is 0.

Since the grad of a function is a derivative, the "mathematical operation" you would use to find A is the anti-derivative or "indefinite" integral.

 

[Nusc]

By "one is given B z-hat" do you mean you are given only the z-component of grad A?


Then there are many solutions. For example, if we are given that the z-component of grad A, then A can be any function of x,y- as long as it has no dependence on z, the z-component of grad A is 0.

No

Since the grad of a function is a derivative, the "mathematical operation" you would use to find A is the anti-derivative or "indefinite" integral.

 

[Nusc]

SOrry folks I meant Curl

 

[nrqed]

SOrry folks I meant Curl

You already have another thread on exactly the same question