# Cross Products

## Homework Statement

Find A
If one is given B z-hat

## The Attempt at a Solution

What mathematical operation would I apply to solve this?

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
Homework Helper
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.

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.

SOrry folks I meant Curl

nrqed