where \(\mu_o = 4\pi \times 10^{-7}\) Tm/A is a universal constant known as the permeability of free space.
ExercisesActivities
The wire shown below carries current \(I\) out of the screen. The circle represents a distance \(R\) away from the wire.
Figure11.2.2.A wire surrounded by four marked test points.
1.Explanation.
Sketch a vector at each marked point to represent the magnetic field. Explain how you determined each vector.
Answer.
Figure11.2.3.The magnetic field around a long straight wire.
2.Calculation.
Determine the magnitude of the magnetic field at each of the marked points.
Answer.
\begin{equation*}
B = \frac{\mu_o I}{2\pi s}
\end{equation*}
3.Sensemaking: Covariational Reasoning.
How does the strength of the magnetic field change as you get farther away from the wire? Explain your reasoning.
Answer.
Since \(s\) is in the denominator, as \(s\) increases the magnetic field strength will decrease!
4.Representation: Vector Field Map.
Use your answers to the above questions to sketch a magnetic field vector map for the region around the wire. Your map should highlight all the major features of the magnetic field you have identified so far.
Answer.
Figure11.2.4.A magnetic field vector map for a long straight wire. The field points in a counter-clockwise direction and gets smaller as you get farther from the wire.
This figure demonstrates the right-hand rule. The wire is held with the right hand so that the thumb points along the current. The fingers wrap around the wire in the same sense as the magnetic field.Figure11.2.5.Some magnetic field lines of a long straight wire. The direction of \(\vec{B}\) can be found with a form of the right-hand rule.
ReferencesReferences
[1]
"Magnetic Field Wire" OpenStax, https://openstax.org/books/university-physics-volume-2/pages/12-2-magnetic-field-due-to-a-thin-straight-wire
