2. For parallel plate capacitor structure, electrostatic forces can be induced i

Question

2. For parallel plate capacitor structure, electrostatic forces can be induced in the length and width direction due to partial alignment of the plates in respective directions. The two forces along the two direction can be expressed as (Trimmer, WS.N., and Gabriel, K., “Design Considerations for Practical Electrostatic Micromotor," Sensors & Actuators, Vol. 11, 1987, pp. 189-206) Fw =Le.crLV2 For a comb-drive shown in the following figure, determine the voltage supply required to pull the moving electrode 12 mm from the unstretched position of the spring. The spring constant k is 0.05 N/m. The comb drive is operated in air. The gap d between the electrodes and the width W of the electrodes are 2 m' and 5 m, respectively Spring constant k / Moving electrodes Stationary electrodes Width of Electrodes, W

Explanation / Answer

Using the equation of Force Balance ->

Force exerted by the Spring in outward direction = Force exerted due to charge attraction by parallel plate capacitors

Spring Force = Spring Constant * Length (from unstretched position)
= 0.05 * 12 * 10-3 N
= 0.6 * 10-3 N

FL = 1/2 * e0er WV2/d
= 1/2 * 8.85 * 10-12 * 1 * 5/2 * V2 (er for air = 1)

Equating both sides ->

0.6 * 10-3 = 0.5 * 8.85 * 2.5 * 10-12 V2

or, V2 = 0.054 * 109

or, V2 = 54 * 106

or, V = 7.3484 * 103 Volts
= 7.34 kV (ans)

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