Chapter 6 Scaling Laws in Miniaturization
Chapter 6 Scaling Laws in Miniaturization
Chapter 6 Scaling Laws in Miniaturization
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nearly as favorably as electrostatic forces.- The electromagnetic forces can be <strong>in</strong>duced <strong>in</strong> a conductor or aconduct<strong>in</strong>g loop <strong>in</strong> a magnetic field B by pass<strong>in</strong>g current i <strong>in</strong> theconductor.- The electromotive force (emf) is the force that drives the electrons-through the conductor.21 φU = (6.13)2 Lwhere φ is the magnetic flux, and L is the <strong>in</strong>ductance.- S<strong>in</strong>ce φ = Li ,1 Li2U =2(6.14)- The <strong>in</strong>duced electromagnetic force would be∂UF =∂x- For constant current case,φ=cons tan ti=cons tan t(6.15a)∂UF = (6.15b)∂x1F = i22∂L∂x20S<strong>in</strong>ce i ∝ l and ∂L/ ∂x∝ l ,4F ∝ l- If 10 times reduction <strong>in</strong> size (l)⇒ Electromagnetic force: 10,000 times reductionComparison: Electrostatic force: only 100 times reductionConclusion: Electromagnetic force is less favorable <strong>in</strong> scale-down thanElectromagnetic force.6.6 <strong>Scal<strong>in</strong>g</strong> <strong>in</strong> Electricity• Examples: Microsystem actuation by electrostatic, piezoelectric, and thermalresistance heat<strong>in</strong>g.• Electric Resistance:LA−1R = ρ ∝ l(6.18)where ρ, L, and A are the resistivity, length, and cross-sectional area, respectively.• Electric Power Loss:PVR21= ∝ l(6.19)7
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