Can the Biot-Savart Law be applied to point P_1 outside a finite wire?

[czmat]

Hi,
I've got a question regarding application of the Biot-savart law along finite wire.
There is a great explenation of this problem in the MIT paper but this does not cover one case.

1. Homework Statement
My question is: does the equation defining magnetic field in point P(x,y) also applies to the point P_1(x,y) (as in the picture below) which is not in boundaries of the wire?

Homework Equations

Magnetic field in point P(x,y) (as in the above figure) along finite wire is:

The Attempt at a Solution

My guess is: yes, just because I can put P_1 coordinates in the equation, but intuition tells me that I am omitting something and unfortunately I don't know what.

 

[kuruman]

My question is: does the equation defining magnetic field in point P(x,y) also applies to the point P_1(x,y) (as in the picture below) which is not in boundaries of the wire?

Yes, but you have to be careful with how you apply Biot-Savart, specifically what is x. You are omitting x₁ from the picture.

 

[czmat]

In that case I would define x as
x=L/2 + x_1

 

[kuruman]

Yes.