Physics Miscellany

Units

• When working with electro-mechanical devices, use of MKSA SI units eliminates the need to work with conversion factors.   That is, a newton-meter quantity of mechanical energy is exactly equal to a volt-ampere-second quantity of electrical energy -- they both equal one joule.
• The interdependence of electrical and mechanical units of measure is demonstrated by the definition of the ampere, the quantity of electrical current.   If one ampere flows through each of two parallel, infinitely thin and infinitely long conductors spaced one meter apart in empty space, the conductors will experience a mechanical force of exactly 0.2 × 10^-6 newtons per meter of conductor length.
• To convert magnetic field intensity in oersteds into SI units of amperes per meter, multiply the oersted quantity by 1000/(4π). For example, 500 Oe = 39 789 A/m.
• To convert magnetic flux density in gauss into SI units of tesla, divide the gauss quantity by 10 000. For example, 4 kG = 0.4 T. (Note: tesla = volt-seconds per square meter.)

Permeability, Permittivity, and the Speed of Light in a Vacuum

• Absolute magnetic permeability is the ratio of magnetic flux density in a medium per unit of magnetic field intensity.   The absolute permeability of a vacuum, µ₀, is defined as 0.4π × 10^-6 volt-seconds per ampere-meter.   One usually finds the units written as H/m or henries per meter.   If a source lists permeability as a dimensionless number, it implies that either 1) CGS units are being used where the permeability is gauss per oersted or 2) that a dimensionless relative permeability is being used.   Multiply this relative permeability by µ₀ to obtain absolute permeability in V-s/A-m.
• The speed of light in a vacuum, c₀, is exactly 299 792 458 meters per second, according to NIST.
• The absolute electric permittivity of a vacuum is defined as ε₀ = 1 / µ₀c₀².   Notice that the units of absolute permittivity are ampere-seconds per volt-meter, usually written as F/m or farads per meter.   Multiply a dimensionless permittivity (also known as a dielectric constant) by ε₀ to obtain absolute permittivity in A-s/V-m.

Force, Stress, Strain, and Pressure

• By convention, tensile force and stress have positive magnitudes.   Conversely, compressive force and stress have negative magnitudes.   Similarly, positive strain indicates a lengthening of a dimension and negative strain indicates a shortening of a dimension.   Zero strain represents the free length of the material.   Hydraulic pressure is a mathematical negative quantity.
• Because they are weak in tension and/or have a quadratic response to a field, many transducing materials are placed under a compressive bias when assembled into a transducer.   The transducer then responds with a near sinusoidal output of force and displacement to a sinusoidal electrical input.   Thus, if negative compressive force and negative compressive stress are impressed at assembly, they produce a negative strain through the material's elastic modulus (at zero field).
• It is common practice to show a strain originating from zero in data taken almost statically.   Note that this is typically a relative zero and does not show the strain induced by mechanical bias.   For a transducing material, plotting several strain versus field curves with a common zero deletes elastic modulus information.   Furthermore, in a dynamic system, the transducing material is subjected to a stress state that changes.   This change in stress state is inseparably linked to the change in strain and field. Plots that show absolute strain as a function of both stress and field enable better dynamic performance predictions.
• Historical note.   Nickel was one of the first practical magnetostrictive materials and is still in use.   It is mechanically biased in tension, since it actually shrinks when subjected to a magnetic field.   In some information sources, this negative strain is assigned a positive magnitude.

Response Time

• A dynamic electro-mechanical system may very well have a microsecond response time on its electrical side.   However, its mechanical side is subject to the response time of all the mechanical dynamics, which tend to be much slower.   Thus, the response of the entire system tends to be limited by the mechanical side.