Answer:
B = (2.8 ± 0.5) 10⁻⁴ T
Explanation:
In this exercise we can approximate the system to a coil, so the magnetic field is
B = μ₀ N / L I
Where N is the number of turns, I the current and L the length
Uncertainty is
ΔB = dB / dI ΔI + dB / dN Δn + dB / dL ΔL
In this case the errors of number of turns are zero
Δn = 0
ΔB = dB / dI ΔI + dB/DL ΔL
ΔB = μ₀ N / L ΔI + μ₀ N I /L² ΔL
ΔB/B = ΔI/I + ΔL/L²
ΔB = (ΔI/I + ΔL/L) B
The value of the magnetic field is
B = 4 π 10⁻⁷ 15 / 0.04 0.6
B = 2.83 10⁻⁴ T
the uncertainty is
ΔB = ( 0.05/0.6 + 0.004/0.04) 2.83 10⁻⁴
ΔB = 0.52 10⁻⁴ T
The result is
B = (2.8 ± 0.5) 10⁻⁴ T
