Rotating B Field: Find Angle for Net Field of 99 nT

[valentinemiss]

Homework Statement

Two concentric circular loops of wire carrying current in the same direction lie in the same plane. Loop 1 has radius 1.8cm and carries 3.6 mA. Loop 2 has radius 2.3cm and carries 6 mA. Loop 2 is to be rotated about a diameter while the net magnetic field set up by the two loops at their common center is measured. Through what angle must loop 2 be rotated so that the magnitude of the net field is 99 nT?

Homework Equations

Bnet = B2 - B1
B1 = u*i / 2R = B2

The Attempt at a Solution

I found B1 to equal 1.26E-7 using the formula above but B2 is where I get stuck. I am not sure where to factor in the angle. I know after I get that figured out I can plug in the values for Bnet and B1 and solve for theta in the B2 formula. You don't need to solve it for me just give me a hint or place to start.

 

[anathema]

Thank you for your question. To solve for B2, you can use the formula B2 = u*i / 2R, where u is the permeability of free space, i is the current in loop 2, and R is the radius of loop 2. However, to incorporate the angle of rotation, you will need to use the formula B2 = u*i / 2R * cos(theta), where theta is the angle of rotation. This is because the magnetic field strength at the center of the loops will vary depending on the angle of rotation. Once you have the value for B2, you can plug it into the formula Bnet = B2 - B1 and solve for theta. I hope this helps. Best of luck with your calculations!