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[2003SM/LNP-06] Lecture-06--What is Thermodynamics and Statistical MechanicsNode id: 5531pageWe begin with scope of thermodynamics and emphasize wide range of its applications. Thermodynamics takes a macroscopic view of a physical system. It laws are based on experience. Statistical mechanics is a microscopic view of physical systems and is based on established laws of classical and quantum mechanics.
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[1998TH/LNP-25]-Efficiency of Carnot EngineNode id: 5595page |
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[NOTES/QM-10001] Representations in an Inner Product SpaceNode id: 4719pageA brief account of representations in a finite dimensional vector spaces is presented. The use of an ortho norrnal basis along with Dirac notation makes all frequently used formula very intuitive. The formulas for representing a vector by a column vector and an operator by matrices are given. The results for change of o.n. bases are summarized.
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[NOTES/QM-20003] Spin Wave Function Node id: 4846page$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$
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[LECS/EM-07002]-Magnetic Field of CurrentsNode id: 5719page |
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21th-hmw-01Node id: 4992page |
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[QUE/EM-02023] EM-PROBLEMNode id: 5126pageUse Gauss's law to find the electric field inside a uniformly charged
solid sphere of radius \(R\) and carrying charged density $\rho$. State facts
other than Gauss's law which you might have used in your answer.
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[QUE/TH-06010] TH-PROBLEMNode id: 5205pageThe specific internal energy of a Van der Waals gas is given by
$$
u=c_v-{a\over v}+\text{const}
$$
Show that
\begin{eqnarray}
c_p-c_v =& R{1\over1-{2a(v-b)^2\over R\theta v^3}}
\end{eqnarray}
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[2019EM/QUIZ-02]Node id: 5352pageElectrodynamics Feb 1,2008
2018 Quiz-II
- Find the direction and magnitude of $\vec{E}$ at the center of a rhombus, with interior angles of $\pi/3$ and $2\pi/3$, with charges at the corners as shown in figure below. Assume that $ q= 1\times 10^{-8}$C, $a=5$cm
-
Two spheres each of radius $R$ are placed so that they partially overlap. Thecharge densities in the overlap region is zero and in the two non overlappingregions is $+\rho$ and $-\rho$ respectively as shown in figure.The separation between the centres of the spheres is $D$.Show that the electric field in the overlap region is constant.
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[2008EM/EVAL-TEST-02]Node id: 5416page |
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[QUE/EM-01013] --- EM-PROBLEMNode id: 5491pageA "dipole" is formed from a rod of length \(2a\) and two charges \(+q\)
and \(-q\). Two such dipoles are oriented as shown in figure at the end,
their centers being separated by a distance \(R\). Calculate the force
exerted on the left dipole and show that, for \(R>>a\), the force is
approximately given by
\[F=\frac{3p^2}{2\pi\epsilon_0R^4}\]
where \(p=2qa\) is the dipole moment.
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[2003SM/Eval-Test-III]Node id: 5559page |
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[PNET/CV-05001] Existence of derivative, analytic property, singular points etc.Node id: 5630pageThe attached file is a collection of questions taken from NET/CSIR/GATE/JEST and other similar examinations
The questions concern:
- Existence of derivative
- Computation of limit
- Checking if a function is analytic or not
- Properties of real and imaginary parts of an analytic function
- Finding real part (or imaginary part) if the other one is given.
KEY CONCEPTS
Existence of derivative, Analytic function, Limit, Cauchy Riemann equations,
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[NOTES/QM-16010] Classical Motion in Three Dimensions Spherically symmetric potentialsNode id: 4802page$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$
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[NOTES/ME-08009]-How good is a frame as inertial framesNode id: 5693page |
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[LECS/EM-10003] -- Energy Conservation ---- Poynting Theorem Node id: 5749pageUsing time dependent Maxwell's equations and considering a charge distribution moving under influence of the electric and magnetic fields, an equation for rate of change of mechanical work done on the charges is derived, see EQ12. This equation is local conservation law of energy. It says that the rate of the sum of change energy of e.m. fields and work done in a volume \(V\) equals to the flow of energy through the boundary of the volume \(V\). The flow though the boundary is given by the Poynting vector \(\vec{S}\) defined in EQ10.
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22-09-10 16:09:51 |
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[QUE/SM-02001] SM-PROBLEMNode id: 5054pageConsider a 2 dimensional phase space ( $q,p$) with a rectangular region defined by four corners as shown.
If the region ABCD is the phase space region at time time t = 0 , find the region $A'B'C'D'$ at time t given the Hamiltonian is
$$ H\,=\,\frac{p^2}{2m}\,-\, m a q $$
and explicitly verify that the area is constant. Take the coordinates of A,B,C and D as $(q_A,p_A)\,,\,(q_B,p_A)\,,\,(q_B,p_C)$ and $(q_A,p_C)$ respectively
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[QUE/TH-06006] TH-PROBLEMNode id: 5179pageConsider a paramagnetic system, with variables magnetization $M$, the magnetic field $B$ and absolute temperature $T$. ( We assume it's dependence on pressure as negligible). The equation of state is ( which will be obtained from statistical mechanics later in the course) is
$$ M\,=\,C\frac{B}{T}, $$
where $C$ is a constant ( referred to as the Curie constant, who had experimentally obtained this relation.
The system's internal energy is ( for a one-dimensional system)
$$ U\,=\,-MB.$$
The work done on the system by external surrounding is $-MdB$
(a) Write the expression for $DQ$ in terms of $dM$ and $dB$
(b) Write the equation for entropy change $dS$ in terms of $dM$ and $dB$
(c) Obtain the entropy $S$
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[2013EM/HMW-09]Node id: 5383page |
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[2003SM/LNP-08] Lecture-08--Basic assumptions of statistical mechanicsNode id: 5533pageStatistical mechanics is based on the fundamental assumption that all microstates of an isolated system are equally
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