Answers:

Part A: $B_{\text{center}} = 1.26 \times 10^{-2} \, \text{T}$

Part B: $B_{\text{axis}} = 2.23 \times 10^{-3} \, \text{T}$

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Here are 5 related questions to explore:

1. What factors affect the magnetic field at the center of a circular coil?
2. How does the number of turns in the coil influence the magnetic field?
3. What would the magnetic field be if the current were doubled?
4. How does the field vary with distance along the axis of the coil?
5. How does the coil’s diameter influence the magnetic field magnitude?

Tip: Always double-check units for consistency when solving magnetic field problems.