Chapter 6 Scaling Laws in Miniaturization

( l)( l)( l )( ll)( l)0 0 1 1 1 23⇒ U ∝= l(6.11)1- A factor of 10 decrease in linear dimension will decrease the potentialenergy by a factor of 1000.• In Fig. 6.6, the electrostatic forces are,FFF∂U∂d- F , F , and F ∝ ( l21 ε ε WLV2 d2r 0d= − = −(2.8)2WL2∂U1 εrε0LV= − =∂W2 d(2.10)2∂U1 εrε0WV= − =∂L2 d(2.11)d W L)- A 10 times reduction in the plate sizes means a 100 times decrease inthe induced electrostatic forces.6.5 Scaling in Electromagnetic Forces• In this section, it is shown that electromagnetic actuation is not scaled down6