Microsphere Size | $2.56\mu m$ |
Beam Strength | $4.6mW$ |
Measurements Per Second | $200$ |
$\Delta t$ between measurements | $.005s$ |
Import Data from .csv file... Add them to arrays.
x_pos = []
y_pos = []
###########################
import csv
with open('C:/Users/Brian/Google Drive/Sophomore/Physics/Advanced Projects Lab 491/2.56 micrometer tracking 5-14-14/2.56 micrometer parsed.csv') as f:
reader = csv.reader(f)
for row in reader:
x_pos.append(float(row[0]))
y_pos.append(float(row[1]))
###########################
# convert lists to arrays for simplified calculations
x_pos = array(x_pos)
y_pos = array(y_pos)
Convert from $\mu m$ to $m$
x_pos = x_pos*10**(-6)
y_pos = y_pos*10**(-6)
$\frac {1}{2} k_b T = \frac {1}{2} k <x^2>$
to compute the variance we must solve...
$variance=\overline{(x_{mean}-x_t)^2}$
x_mean = mean(x_pos)
y_mean = mean(y_pos)
x_var = mean((x_mean - x_pos)**2)
y_var = mean((y_mean - y_pos)**2)
print("The x variation is " + str(x_var))
print("The y variation is " + str(y_var))
The x variation is 6.92133033795e-16 The y variation is 2.57011754526e-15
x var | 6.92133E-16 m |
y var | 2.57012E-15 |
$\ \frac {k_b T}{<x^2>} = k $
kb = 1.3806488e-23
T = 298
x_strength = (kb*T)/x_var
y_strength = (kb*T)/y_var
Let's convert from standard units to piconewtons per micrometer
x_strength = x_strength*(10**12)/(10**6)
y_strength = y_strength*(10**12)/(10**6)
x_strength # piconewtons/micrometer
5.9444257434757573
y_strength # piconewtons/micrometer
1.6008347289755338
direction | k |
---|---|
x trap strength | $5.94 \frac {pN}{\mu m}$ |
y trap strength | $1.60 \frac {pN}{\mu m}$ |