turan, ALTUG OZPINECI, Tezek, İlker Ümit UZUN KAYMAK, Jane Smith, IBRAHIM GUNAL, SELAHATTIN OZDEMIR, sinanbilikmen, HANDE TOFFOLI, STAFF, Bulent akinoglu, Bayram Tekin
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The Zeeman Effect
Spacing between successive line without a magnetic field
2
a=20 x 1 0 [ mm]
Magnet Current
I [A]
Magnetic Field
Strength [T]
Spacing between 2
extreme lines
Spacing between
successive lines
2 a [ x 1 0 mm]
a [x 1 0 mm ]
a
a
2
2
18
0,494
PHYS307 Applied Modern Physics
THE SPECTROSCOPY OF BETA PARTICLES
Mert AVCI 1909936
Experiment Date: 28.03.2017
Report Submit Date: 04.04.2017
Counts at B=0
Trial 1
8
Trial 2
6
Table: Counts at zero magnetic field strength for
90
Average Counts
7
Sr .
B[T
PHYS307 Applied Modern Physics
Exp. THE PHOTOELECTRIC EFFECT
Mert AVCI
1909936
Experiment Date: 11.04.2017
Report Submit Date: 18.04.2017
Table 1: Currents versus voltages for the light having constant wavelength at different intensities
=436 nm
2mm
4mm
8
Filament Voltage: 6.0 V
Filament Voltage: 8.0 V
Collector Voltage: 2.0 V
Collector Voltage: 1.5 V
Oven Temperature: 188C Oven Temperature: 186C
Voltage at first minimum/maximum [V]
Voltage at second minimum/maximum [V]
Voltage at third minimum/maximum [V]
PHYS 426
HW 4 / SUGGESTED HW PROBLEMS/ Total: 6 PROBLEMS
1. A Q-switched laser uses a cavity with a length of 1m and an average mirror reflectivity of r = 0.9.
The gain medium is an Nd:YAG crystal, which is pumped by a flashlamp.
a) Draw the optical confi
Mathematical Theory of
Electromagnetism
Piero Bassanini
University of Rome, La Sapienza Rome, Italy
[email protected]
Alan Elcrat
Wichita State University, Wichita, Kansas
[email protected]
DOI: 10.1685/SELN09001 - Vol. 2 - 2009
Licensed u
Quick calculus
Daniel OConnor
These notes are intended to be a quick summary of some of the key
intuition behind calculus. The notes are not self-contained and are meant
only to supplement a calculus class, not to stand alone. Moreover, the
notes are a wo
Gradient, Divergence and Curl
in Curvilinear Coordinates
Although cartesian orthogonal coordinates are very intuitive and easy to use, it is often found
more convenient to work with other coordinate systems. Being able to change all variables and
expressi
Instructor: Longfei Li
Math 243 Lecture Notes
14.6 Directional Derivatives and the Gradient
We knew about the partial derivatives fx and fy from previous lectures:
fx represents the rate of change of z in the positive x direction (i)
fy represents the rat
Instructor: Longfei Li
Math 243 Lecture Notes
16.2 Line Integrals
The invention of line integrals is motivated by solving problems in fluid flow, forces, electricity and
magnetism.
Line Integrals of a Function
We can integrate a function over any curve C,
"/'
Differential Geometry
Some Problems
Space Curves I
Reminder:
Tangent vector:
T = C ( s ) = ( x ( s ), y ( s), z ( s )
Curvature normal:
N = C( s )
Torsion and bi-normal:
B =T N
= N B
1
Amir Vaxman 2011
"/'
Space Curves I
Exercise: Find the
Instructor: Longfei Li
Math 243 Lecture Notes
16.6 Parametric Surfaces and Their Areas
Parametric Surfaces
Recall a space curve can be parametrized by a vector function r(t) of single variable t. Similarly, we
can parametrize a surface by a vector functio
Integration using
trig identities or
a trig substitution
Some integrals involving trigonometric functions can be evaluated by using the trigonometric
identities. These allow the integrand to be written in an alternative form which may be more
amenable to
Instructor: Longfei Li
Math 243 Lecture Notes
16.7 Surface Integrals
Definition: The surface integral of f (x, y, z) over the surface S is
ZZ
f (x, y, z) dS =
S
lim
m,n
m X
n
X
f (Pij )Sij
i=1 j=1
ZZ
f (r(u, v)|ru rv | dA
=
D
ZZ
=
r
r
f (x(u, v), y(u, v
Instructor: Longfei Li
Math 243 Lecture Notes
15.2 Iterated Integrals
Let f be an integrable function of 2 variables over the rectangle region R = [a, b] [c, d]. Integrate
f (x, y) w.r.t. y (fixing x) from c to d:
d
Z
A(x) =
f (x, y)dy
c
Then, integrate A
Instructor: Longfei Li
Math 243 Lecture Notes
16.1 Vector Fields
A vector field on R2 is a function F~ that assigns to each point (x, y) D R2 a two-dimensional
vector F~ (x, y).
F~ is a vector so we can write it in its components
F~ (x, y) =< P (x, y), Q(
MIT OpenCourseWare
http:/ocw.mit.edu
18.02 Multivariable Calculus
Fall 2007
For information about citing these materials or our Terms of Use, visit: http:/ocw.mit.edu/terms.
18.02 Lecture 11.
Tue, Oct 2, 2007
Dierentials.
Recall in single variable calcul
Instructor: Longfei Li
Math 243 Lecture Notes
14.1 Function of Several Variables
Function of Two Variables
Definition: A function of 2 variables is a rule that assigns to each ordered paired of real numbers
(x, y) in a set D a unique real number denoted b
Instructor: Longfei Li
Math 243 Lecture Notes
16.3 The Fundamental Theorem for Line Integrals
Theorem Let C be a smooth curve given by r(t), a t b. Let f be a differentiable function of 2 or
3 variables whose gradient vector f is continuous on C. Then
Z
f
Instructor: Longfei Li
Math 243 Lecture Notes
13.1 Vector Functions and Space Curves
A vector valued function (vector function) is a function whose domain is a set of real numbers and
whose range is a set of vectors.
The vector function in 3D is denoted b
Instructor: Longfei Li
Math 243 Lecture Notes
15.3 Double Integrals over General Regions
So far, we learned how to integrate over rectangular regions. However, we want to integrate over more
general regions.
Type I : If f is continuous on a region D such