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Question: 1 a 2 m diameter glass bead has a surface...

Question details

1. A 2 µm diameter glass bead has a surface charge of 1 fC. How many SiO– groups are on the bead's surface?

2. An electric field is applied to this bead, using two wires whose ends are positioned 2 cm apart and are then hooked up to a 4V power supply.

3. What electric field does this produce, in V/m?

4. How large a force (in pN) does this voltage produce on the charged bead?

5. How fast would this bead move through water? Hint: use the Stokes drag formula for a sphere at low Re, which is the appropriate regime here, with a viscosity of 9x10–4 Pa.s for water. Give your answer in µm/s.

6. Put together your responses to the last few questions into an equation that relates the applied voltage ΔV to the resulting bead speed v, in terms of L, the distance between the wires; D, the diameter of the bead; µ, the viscosity of water; and q, the charge on the bead.

v = qΔV / 3πµDL
v = 3πµDLqΔV
v = 3πµDL / qΔV
v = 3µqΔV / DL
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