Magnetic field using the Biot-Savart Law

[w3390]

Homework Statement

A small current element at the origin has a length of 2.0mm and carries a current of 2.0A in the +z direction. Find the magnitude and direction of the magnetic field due to this current element at the point (0,3.0m,4.0m).

Homework Equations

Biot-Savart Law: dB=(mu/4pi)(Idl cross r(hat))/(r^2)

The Attempt at a Solution

I attemped the problem by integrating the biot-savart law holding everything constant except for dl. However, this does not give me the correct answer, which by the way is -9.6pT in the +i direction.

 

[hage567]

Please show more detail of what you've done. It is impossible to guess what you did and where you went wrong.

 

[w3390]

I can't really show more work because I thought I only had to do a simple integration holding everything constant except for dl. But, I know that dl cross r hat will be in the negative i hat direction. In my equation, I am using 4pi*10^-7 for mu, 2A for I, .002m for l, and .05 for r. Do I need to take into account the dependence r has on the segment dl?

 

[hage567]

Do I need to take into account the dependence r has on the segment dl?

I don't think so in this case since the length of the current element is so small compared with the distance to your point of interest (although normally you would consider it). You could always try it both ways. Maybe your teacher wants you to do it the more rigorous way, though.

You have r=0.05, is that not supposed to be 5?

I think one thing you are missing is that there is an angle between dl and r hat (think cross product).