Magnetic field due to two loops

[Physicslearner500039]

Homework Statement

In Fig. 29-45, two concentric circular loops of wire carrying current in the same direction lie in the same plane. Loop 1 has radius 1.50 cm and carries 4.00 mA. Loop 2 has radius 2.50 cm and carries 6.00 mA. Loop 2 is to be rotated about a diameter while the net magnetic field B 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 that net field is 100 nT?

Relevant Equations

B = (μ * Φ * i)/(4*π*r) magnetic field due to circular loop.

My attempt is the magnetic field due to loop1 and loop2 should get added
The magnetic field due to loop1 is
B1 =(μ0 * Φ * i)/(4*π*r) = (4*π*(2*π)*0.004) /(4 *π*0.015) = 1670nT.
I assumed this value should be less than 100nT. What is the reason?
The other question is "Loop 2 is to be rotated about a diameter?" Even if i rotate by any angle Φ will always be 2π as long as it is complete circle. Am I correct? Please advise.

 

[TSny]

The magnetic fields are vector quantities. When you rotate loop 2, what happens to the direction of B₂?

 

[gneill]

Using the formula for the magnetic field at the center of a circular loop (see http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/curloo.html):
$$B = \frac{\mu_o I}{2 R}$$
I found $B_1$ to be 167.5 nT.

So, not sure what happened in your calculation. I haven't seen the form of equation you've used before (with the $\Phi$ term).

 

[TSny]

I haven't seen the form of equation you've used before (with the $\Phi$ term).

I had to think about that, too. I believe the formula given in the first post is for finding B at the center of a circular arc that subtends an angle Φ. The full circular loop is a special case.

 

[gneill]

I had to think about that, too. I believe the formula given in the first post is for finding B at the center of a circular arc that subtends an angle Φ. The full circular loop is a special case.

Ah! That makes sense! Thanks for doing my thinking for me