# Magnetic field strength in two wires

1. Multiple choice problem, the prompt is the following: Two wires carry currents is opposite directions, as shown below. The wires are separated by a distance of 0.02 meter, and points P and Q are located 0.01 meter above and below the bottom wire.

Compare the Magnetic field strength at point Q to the magnetic field strength at point P.
a. Bp=Bq
b. Bp= (1.2)Bq
c. Bp= (1/4)Bq
d. Bp= (1/9)Bq
e. Bp= 3Bq

2. I understand from a previous problem that the magnetic field at point P from the top wire is B=(10μ)/∏ (simplified from the equation B=(μI)/2∏r), but I'm having trouble understanding if the magnetic field strength at point Q should be from both of the wires or just the top wire.

3. My initial thought was to add the magnetic field due to the top wire and the magnetic field due to the bottom wire together to get the strength at point Q, but I'm not sure if my math is wrong or what, because I get B= (μ.2)/∏.06 from the bottom wire which simplifies to (μ(10/3))/∏. add that to what I got for the the magnetic field with a radius of .01 and you get (2μ(40/10))/2∏. I'm not sure if I'm going crazy because I'm tired or what, but please please please help me! Thank you so much!

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For point P, you calculated the field only due to the TOP wire, you should calculate the field due to the bottom wire as well, and add them up as vectors (hint: to find the direction of the field, use the right hand rule). For point Q, your calculation for the field due to the bottom wire is a bit off, the distance from point Q is clearly 0.01 meters from the bottom wire, and 0.03 meters from the top one, use those values for $r$ and don't forget to include the direction of both fields when adding them.