Turns per metre for 1 mT

Problem

Estimate the number of turns per metre needed to obtain, inside an air-core solenoid, a magnetic field $B = 1$ mT with a current $i = 1$ A. Is the value reasonable for a winding made in a laboratory with $1$ mm copper wire?

Solution

For a solenoid $B = \mu_0\,n\,i$, with $n = N/L$ the number of turns per metre. Solving for $n$: $n = \frac{B}{\mu_0\,i} = \frac{10^{-3}}{4\pi\cdot 10^{-7}\cdot 1} \approx 8\cdot 10^2$ $\ev{n \sim 10^3\;\text{turns/m}}$ With $1$ mm diameter copper wire, up to about $1000$ turns per metre can be wound side by side: the value found is therefore achievable in a laboratory winding.

Links

Topics: Magnetism Concepts: Magnetic field Skills: Fermi estimation