Tasks

1. Measure the magnetic field of a solenoid at 5 points along the axis.
2. Choose a formula to model the solenoid’s magnetic field and compare predictions to the measured values.

Resources

• Solenoid
  • Specifications for Science First Air Core Solenoid
  • NOTE: do not exceed 5A current
• Power supply
• Tesla meter
• Ruler

Background

A solenoid is a coil of wire used to produce a magnetic field. The field on the center axis of a very long solenoid can be assumed to be constant and axial, and can be solved for using Ampere’s Law, as shown in the diagram, to be B_z = \mu_0 n I where n is the number of turns per unit length, I is the current, and \mu_0=4\pi \times 10^{-7} \mathrm{\ N/A^2} is the magnetic constant or vacuum permeability.

For a physical solenoid of length L and radius R where the radius is greater than the length, the magnetic field strength along the axis can be approximated by B_z=\frac{\mu_0 I N R^2}{2(R^2+z^2)^{\tfrac{3}{2}}}

In cases where the length is larger than the radius, up to roughly  L/R<100, the z-component along the axis can be estimated as B_z=\frac{mu_0NI}{2}\left( \frac{L/2-z}{L\sqrt{R^2+(L/2-z)^2}} + \frac{L/2+z}{L\sqrt{R^2+(L/2+z)^2}} \right)

Formulas for off-axis points around a solenoid are more complicated, as they include radial components in addition to the z-component.