CE Four lightweight, plastic spheres, labeled A, B, C, and D, are suspended from threads in various combinations, as illustrated in Figure 19-47 . It is given that the net charge on sphere D is + Q , and that the other spheres have net charges of + Q , − Q or 0. From the results of the four experiments shown in Figure 19-47 , and the fact that the spheres have equal masses, determine the net charge of (a) sphere A , (b) sphere B, and (c) sphere C.
CE Four lightweight, plastic spheres, labeled A, B, C, and D, are suspended from threads in various combinations, as illustrated in Figure 19-47 . It is given that the net charge on sphere D is + Q , and that the other spheres have net charges of + Q , − Q or 0. From the results of the four experiments shown in Figure 19-47 , and the fact that the spheres have equal masses, determine the net charge of (a) sphere A , (b) sphere B, and (c) sphere C.
CE Four lightweight, plastic spheres, labeled A, B, C, and D, are suspended from threads in various combinations, as illustrated in Figure 19-47. It is given that the net charge on sphere D is +Q, and that the other spheres have net charges of +Q, −Q or 0. From the results of the four experiments shown in Figure 19-47, and the fact that the spheres have equal masses, determine the net charge of (a) sphere A, (b) sphere B, and (c) sphere C.
Curve Fitter
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FILE
DATA
FIT TYPE
FIT
Harmonic Motion X
us
0.45
mi
ce
0.4
0.35
0.3
0.25
0.2
Residuals Plot
Contour Plot
Plot Prediction Bounds None
VISUALIZATION
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COA Fourier
Equation
Fit Plot
x vs. t
-Harmonic Motion
a0+ a1*cos(x*w) +
b1*sin(x*w)
Number of terms
Center and scale
1
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Results
Value
Lower
Upper
0.15
a0
0.1586
0.1551
0.1620
a1
0.0163
0.0115
0.0211
0.1
b1
0.0011
-0.0093
0.0115
W
1.0473
0.9880
1.1066
2
8
10
t
12
14
16
18
20
Goodness of Fit
Value
Table of Fits
SSE
0.2671
Fit State Fit name
Data
Harmonic Motion x vs. t
Fit type
fourier1
R-square
0.13345
SSE
DFE
0.26712
296
Adj R-sq
0.12467
RMSE
0.030041
# Coeff
Valic
R-square
0.1335
4
DFE
296.0000
Adj R-sq
0.1247
RMSE
0.0300
What point on the spring or different masses should be the place to measure the displacement of the spring? For instance, should you measure to the bottom of the hanging masses?
Let's assume that the brightness of a field-emission electron gun is given by
β
=
4iB
π² d²α²
a) Assuming a gun brightness of 5x108 A/(cm²sr), if we want to have an electron beam with a
semi-convergence angle of 5 milliradian and a probe current of 1 nA, What will be the
effective source size? (5 points)
b) For the same electron gun, plot the dependence of the probe current on the parameter
(dpa) for α = 2, 5, and 10 milliradian, respectively. Hint: use nm as the unit for the
electron probe size and display the three plots on the same graph. (10 points)
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