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[NOTES/EM-03004]-The Electric Stress TensorNode id: 5641pageAn expression for the electric stress tensor is derived for a charge distribution in a volume \(V\). The surface integral of the stress tensor gives the total electric force on the charge in the volume \(V\).
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[NOTES/QM-17004] Recurrence Relations for CG CoefficientsNode id: 4817page$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$
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22-03-04 09:03:38 |
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[NOTES/ME-14007]-Parallel Axes TheoremNode id: 5701page |
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22-08-16 16:08:43 |
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[NOTES/EM-12001]-Lorentz transformations Node id: 5757page
The basic equations of Maxwell's theory are written down in relativistic notation. Using Lorentz transformations of the potentials, the expressions of the scalar and vector potentials of a point charge moving with a uniform velocity are obtained.
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23-03-03 21:03:55 |
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[QUE/SM-03005] --- SM-PROBLEMNode id: 5069pageA system consists of three particles and each particle can exist in five possible states. Find the total number of microstates and the number of microstates that energy level has two particles assuming
- the particles are non-identical
- are identical bosons
- are identical fermions.
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22-01-09 20:01:30 |
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[QUE/TH-13002] TH-PROBLEMNode id: 5187pagea) An ion of mass m and electric charge e is moving in a dilute gas of molecules with which it collides. The mean time between collisions is $\tau$. Let there be a uniform electric field $E$ along the x-axis. Show that the mean distance travelled by the ion is
$$ \frac{Ee}{m}\tau^2$$
assuming the velocity of the ion is zero immediately after collision.
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[2003SM/LNP-16] Lecture-16--Open Systems —Grand Canonical EnsembleNode id: 5541page |
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22-07-07 07:07:09 |
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[1998TH/LNP-36]-Statistical MechanicsNode id: 5605page |
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[NOTES/QM-11006] Optics Mechanics Analogy Road to Wave MechanicsNode id: 4734page$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}\newcommand{\matrixelement}[3]{\langle#1|#2|#3\rangle}\newcommand{\PP}[2][]{\frac{\partial^2 #1}{\partial #2^2}} \newcommand{\dd}[2][]{\frac{d#1}{d#2}} \newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}} \newcommand{\average}[2]{\langle#1|#2|#1\rangle}$
Making use of analogy between optics ad mechanics we motivate the introduction of the Schrodinger equation.
Here Fermi's "Lectures on Quantum Mechanics" has been followed very closely..
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24-06-23 18:06:17 |
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[NOTES/ME-06001a]-Energy ConservationNode id: 5673page$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$
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22-08-14 09:08:56 |
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Thermodynamics --- Notes For Lectures and Problems [TH-MIXED-LOT]Node id: 4890collection |
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22-04-12 22:04:24 |
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[NOTES/EM-09008]-Conductor Moving in Magnetic FieldNode id: 5729pageThe electrons in a conductor are free to move. So when a conductor moves in a magnetic field, the electrons experience a force and the e.m.f. is just the work done by the magnetic force. We illustrate this by means of an example.
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22-08-24 17:08:06 |
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Quantum Field Theory --- Notes for Lectures and Problems --- MIXED-LOT Node id: 5011multi_level_page |
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[QUE/TH-03001] TH-PROBLEMNode id: 5154pageConsider \(N\) molecules of a gas obeying van der Waals
equation of state given by
\[\left(P+ \frac{a N^2}{V^2}\right)\big(V-Nb\big)
= Nk_B T\]
where \(a\) is a measure of the attractive forces between
the molecules and \(b\) is another constant proportional to
the size of a molecule. The other symbols have their
usual meanings. Show that during an isothermal expansion (Temperature is kept
constant) from volume \(V_1\) to
volume \(V_2\) quasi-statically and reversibly, the work done is
\[ W =-Nk_B T \log\left(\frac{V_2-Nb}{V_1-Nb}\right) + a^2
\Big(\frac{1}{V_1}-\frac{1}{V_2}\Big)\]
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22-01-13 18:01:03 |
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[QUE/TH-07009] TH-PROBLEMNode id: 5215pageTen grams of water at 20$^\circ$C is converted into ice at
-10$^\circ$C at constant atmospheric pressure. Assuming the heat
capacity per gram of liquid water to remain constant at 4.2 J/g\,K,
and that of ice to be one half of this value, and taking the heat of
fusion of ice at 0$^\circ$C to be 335 J/g, calculate the total
entropy change of the system.
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22-01-23 11:01:19 |
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[NOTES/EM-02010] Gauss Law and Use of SymmetryNode id: 5956pageGauss law aloe is not sufficient to determine the electric field for a given system.To determine electric field using Gauss law the symmetry of problem plays an important role by determining the direction of the electric field in given problem.
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23-10-18 19:10:36 |
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[2019EM/QUIZ-10]Node id: 5362pageElectrodynamics Apr 8, 2019
Quiz-X
- At the upper surface of the Earth’s atmosphere, the time-averaged magnitude of the Poynting vector \(<S> =1.35^10^{W/m}^2\) is referred to as
the solar constant.
- Assuming that the Sun’s electromagnetic radiation is a plane sinusoidal wave, what are the magnitudes of the electric and magnetic fields?
- What is the total time-averaged power radiated by the Sun? The mean Sun-Earth distance is \(R =1.50\times10^{11}\) m .
- Following equation contains the complete information about the electromagnetic wave \begin{equation*} \vec{E}(z,t)=E_0\sin(kz-\omega t)\hat{i} \end{equation*} Find the directions of wave propagation, wavelength, frequency, speed of propagation, magnetic field, the Potynting vector and the intensity of the wave.
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22-04-04 17:04:27 |
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[2018EM/HMW-05]Node id: 5426page |
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22-06-21 08:06:40 |
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[NOTES/EM-01003]-Thomson’s parabola methodNode id: 5507pageThe parabola method was used to measure charge to mass ratio of the electron by measuring the deflection of the electrons when they pass through a uniform electric field. The method is described here and an expression for \(e/m\) in terms of the deflection of the electron.
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23-03-17 18:03:37 |
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[NOTES/EM-02007]-Maxwell's Equations for Electrostatics-INode id: 5579pageThe Gauss law of electrostatics follows from the Coulomb’s law for a point charge and superposition principle. The Gauss law along with the Gauss divergence theorem of vector calculus imply Maxwell’s first equation \(\nabla\cdot\bar{E}=\rho/\epsilon_0\) for electrostatics
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23-10-10 20:10:14 |
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