Question

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

Answer 1

B = (2.8 ± 0.5) 10⁻⁴ T

Step-by-step 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