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Magnetic Units of Measurement
16 questions By Tony R. Kuphaldt
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Question 1 of 16
In electric circuits, the three basic quantities are voltage (E or V), current (I), and resistance (R), corresponding to the general concepts of cause, effect, and opposition, respectively.
I = E Reffect = cause opposition
Magnetic “circuits” also have quantities corresponding to “cause,” “effect,” and “opposition.” Identify these quantities, along with their respective symbols, and write an “Ohm’s Law” equation relating them mathematically. Also, identify the units of measurement associated with each, in three systems of measurement: CGS (“old” metric), SI (“new” metric), and English.
Reveal answer“Cause” = Magnetomotive force (MMF) = F
“Effect” = Magnetic flux = Φ
“Opposition” = Reluctance = ℜ
This relationship is known as Rowland’s Law, and it bears striking similarity to Ohm’s Law in electric circuits:
Φ = F ℜ
Follow-up question: algebraically manipulate the Rowland’s Law equation shown above to solve for F and to solve for ℜ.
Notes:Magnetism, while commonly experienced in the form of permanent magnets and magnetic compasses, is just as “strange” a concept as electricity for the new student. At this point in their education, however, they should be familiar enough with voltage, current, and resistance to reflect upon them as analogous quantities to these new magnetic quantities of MMF, flux, and reluctance. Emphasize the analogical similarities of basic electrical quantities in your discussion with students. Not only will this help students understand magnetism better, but it will also reinforce their comprehension of electrical quantities.
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Question 2 of 16
If we were to graph the “response” of a resistor to various levels of applied voltage, we would obtain a plot that looks like this:
If we were to graph the “response” of a ferromagnetic sample to various levels of applied magnetomotive force, we would obtain a plot that looks something like this:
What does this graph indicate to you, as compared to the graph for a resistor’s characteristics? What is the significance of this with regard to magnetic “circuit” analysis?
Reveal answerThe MMF/flux plot for a ferromagnetic material is quite nonlinear, unlike the plot for an electrical resistor.
Notes:Ask your students to identify resistance on the V/I graph shown in the question. Where on that graph is resistance represented? Your more mathematically astute students will recognize (or perhaps recall from earlier discussions) that the slope of the plot indicates the resistance of the circuit. The less resistance, the steeper the plot (at least in this case, where current is on the vertical axis and voltage on the horizontal). At any point on the plot, the slope is the same, indicating that resistance does not change over a wide range of voltage and current.
Now, direct their attention to the MMF/flux graph. Where is reluctance indicated on the graph? What conclusion may we form regarding reluctance in a magnetic circuit, from analyzing the shape of the MMF/flux curve shown? At what point is reluctance the greatest? At what point is it the least?
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Question 3 of 16
Suppose that a length of electrical wire is wrapped around a section of an iron torus, and electric current conducted through the wire:
What factors influence the amount of MMF, flux, and reluctance in this magnetic “circuit”?
Reveal answerMMF is determined by the amount of current through the wire coil, and the number of turns in the coil (F = I N). Reluctance is determined by the cross-sectional area of the magnetic flux path, the length of that path, the type of material the torus is made of, and the amount of flux present in the torus. Magnetic flux is determined by the MMF and reluctance.
Follow-up question: how similar are these relationships to voltage, resistance, and current in an electrical circuit? Note any similarities as well as any differences.
Notes:Perhaps the most interesting part of the answer to this question is that magnetic reluctance (ℜ) changes with the amount of flux (Φ) in the “circuit”. At first, this may seem quite different from electrical circuits, where resistance (R) is constant regardless of current (I).
However, the constancy of electrical resistance is something easily taken for granted. Ask your students to think of electrical devices (or phenomena) where resistance is not stable over a wide range of currents. After some discussion, you should find that the phenomenon of constant resistance is not as common as one might think!
After students have grasped this concept, ask them what it means with regard to magnetic flux (Φ) versus MMF (F). In other words, what happens to flux in a magnetic circuit as MMF is increased?
