How to Find the Magnetic Field Gradient from Four Parallel Wires?

[Niles]

Homework Statement

Hi

I am looking at four parallel wires of finite length L, whose currents run in the directions shown in the attached figure. There is no gradient along the wire-axis, so from Maxwell's equation
$$\frac{dB_x}{dx} = -\frac{dB_y}{dy} \equiv \tilde B.$$
How would I go about finding an expression for the gradient $\tilde B$ given some current I though the wires? This isn't a homework question, I have just not been able to find the answer anywhere.


Niles.

 

[berkeman]

Homework Statement

Hi

I am looking at four parallel wires of finite length L, whose currents run in the directions shown in the attached figure. There is no gradient along the wire-axis, so from Maxwell's equation
$$\frac{dB_x}{dx} = -\frac{dB_y}{dy} \equiv \tilde B.$$
How would I go about finding an expression for the gradient $\tilde B$ given some current I though the wires? This isn't a homework question, I have just not been able to find the answer anywhere.


Niles.

I'm not seeing the figure...?

 

[Niles]

Sorry, I'll upload it in just a few minutes. Thanks for letting me know.

EDIT: I have attached it now. Thanks.