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224 6 Answers, Hints and Solutions
Chapter 5

A5.1 Figure A.15 shows a simulated result, indicating that the force decreases
inversely proportional to the particle diameter (a), and linearly increases with
temperature (b). At less than 10 nm in diameter, it reaches the piconewton
(pN) order

(a) (b)
8 10 -13 d=100 nm
Force F due to Brownian motion (N) 10 -12 0.39 pN Force F due to Brownian motion (N) 6 10 -13
T= 298 (K)
-11
10
-13
7 10
d=40 nm
d=20 nm
-13
5 10
-13
4 10
0.20 pN
-13
-13
3 10
10
-13
1 10
10 -14 0.08 pN 2 10 -13
1 10 100 1000 280 300 320 340 360 380
Diameter d (nm) Medium temperature T (K)
Fig. A.15. Relationships between force due to Brownian motion and diameter of
microsphere (a), and temperature of medium (b)

A5.2 See Fig. A.16 and [5.20].

Metalic probe

Dielectric
Plane wave prism

Fig. A.16. 3-D configuration of system for calculation of scattered light by sharp-
ened metal probe [5.20]