When trying to determine the maximum magnetic field created by a 15-turn circular coil, you measure the maximum current to be 0.6±0.05 A, and the radius of your coil to be 0.04±0.004 m. If these are the only uncertainties, what is the uncertainty in the maximum magnetic field due to just the uncertainty in the current

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

c. magnitude and direction