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Question: A nanobridge is formed of a rigid platform having the dimensions of 200 nm # 200 nm # 2 nm and two identical nanowires of diameter 120 nm and length 30 nm made of a material with E = 140 GPa, G = 100 GPa, and t = 5400 kg/m3 (assume both the plate and nanowires are made of the same material). Decide which of the following two resonance shift methods is more sensitive in detecting a mass quantity of 2 # 10-14 kg:
(a) Bending mode with mass deposited at the center of the plate; the damping coefficient in translation is ct = 4 # 10-9 N-s/m;
(b) Torsional mode with mass deposited off the plate center at a distance of 100 nm; the damping coefficient in rotation is cr = 5 # 10-6 N-m-s. Draw the transmissibility curve for each case assuming sinusoidal input displacement of the base is applied in bending and sinusoidal input rotation of the base is applied in torsion.
A sphere of radius R is uniformly charged to a total charge of Q. It is made to spin about an axis that passes through its center with an angular speed ω. Find the magnitude of the resulting magnetic field at the center of the sphere.
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