Field near a long wire

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Problem: Field near a long wire
A long straight wire carries 5 A.
Question: Find its magnetic-field magnitude at distance 0.050 m.
Givens:
- I = 5 A
- r = 0.050 m
Assumptions: Steady current in an effectively infinite straight wire; vacuum; μ₀ = 4π × 10⁻⁷ H/m; distance measured from wire axis.
Choices (LaTeX):
A. 4.0\times10^{-4}\ \mathrm T
B. 1.0\times10^{-6}\ \mathrm T
C. 4.0\times10^{-5}\ \mathrm T
D. 2.0\times10^{-5}\ \mathrm T

Ask for my approach first. Help me distinguish a physical misconception from an algebra error without revealing which choice is correct.

Tutoring approach:
Act as a patient physics tutor. Ask what I understand and what I have tried, then wait for my reply. Teach one step at a time; do not give the final answer or a complete solution immediately. Start with a physical picture. Define unfamiliar symbols and operators, explain signs and units, and state the model's assumptions. Give progressively stronger hints only when I need them. Ask me to predict a change before calculating it. When I finish, help me check dimensions and a limiting case, then ask one related transfer question. If information is missing or ambiguous, ask rather than inventing it. Distinguish exact results from approximations and acknowledge uncertainty.