Magnetism
Beginner
Magnetic Field of Current
Source: High school physics (Chinese)
Problem Sets:
magnetic field
Problem
A solenoid is $L = 1.0 \text{ m}$ long with average diameter $D = 3.0 \text{ cm}$. It has $5$ layers of windings with $850$ turns per layer, and carries a current $I = 5.0 \text{ A}$. Find the magnetic flux density at the center of the solenoid.
$B = \mu_0 n I \approx 2.67 \times 10^{-2}$ T $\approx 0.027$ T, directed along the solenoid axis.
Total number of turns: $N = 5 \times 850 = 4250$.
Turns per unit length: $n = \dfrac{N}{L} = \dfrac{4250}{1.0} = 4250 \text{ turns/m}$.
Since $L \gg D$, the long-solenoid approximation gives a uniform interior field:
$$B = \mu_0 n I = (4\pi \times 10^{-7})(4250)(5.0) \approx 2.67 \times 10^{-2}\text{ T}$$(Multiple layers don't change the formula — only the total turns per unit length $n$ matters at the central axis.)