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kapoor kapoor's picture 4 hours 17 min ago

Problem/EM-05005

Consider a point charge \(q\)  embedded in a semi-infinite dielectric medium of dielectric ) constant  \(\epsilon_1\), and located a distance  from a plane interface that separates the first medium from another semi-infinite dielectric medium of dielectric constant  \(\epsilon_2\). Suppose that the interface coincides with the plane. Find the electric field everywhere if the distance of the point charge from the interface is \(d\).

kapoor kapoor's picture 8 hours 14 min ago

Problem/EM-05003/Point charge and a dielectric plate

A point charge and a dielectric plate of permittivity  \(\epsilon_2\) are embedded in a dielectric medium of permittivity  \(\epsilon_1\). as shown in figure 2. Use method of images and find electric field everywhere.

kapoor kapoor's picture 8 hours 39 min ago

\(\maltese\) Problem/QM-05031 Temperature for Fusion Process in the Sun

Consider an ionised plasma of protons in thermal equilibrium. Assuming a Maxwell-Boltzmann distribution, estimate the temperature required for two protons to overcome the Coulomb barrier for fusion assuming an approach distance of 1 fm. Compare this with the temperature when quantum effects come into play. For this, use the distance between the two protons as the de-Broglie wavelength at which Coulomb energy becomes equal to the kinetic energy of the protons.   Click for Solution


       Source:Sarita Vig

kapoor kapoor's picture 1 day 15 hours ago

\(\maltese\) Solved Problem/QM-05031-SOL

Consider an ionised plasma of protons in thermal equilibrium. Assuming a Maxwell-Boltzmann distribution, estimate the temperature required for two protons to overcome the Coulomb barrier for fusion assuming an approach distance of 1 fm. Compare this with the temperature when quantum effects come into play. For this, use the distance between the two protons as the de-Broglie wavelength at which Coulomb energy becomes equal to the kinetic energy of the protons.  

See attached document for solution.

kapoor kapoor's picture 2 days 15 hours ago

Repository of Questions, Problems and More

\(\require{\amssymb}\)

This  page has links to Short Questions and Problems in all areas.
These are classified into several groups. The groups are

  1. Recall and understanding levels
  2. Application and Analysis Levels
  3. Synthesis and Judgement Creativity
  4. Mixed Bag

The first three groups make use of Bloom's Taxonomy.
The Mixed Bag correspond to those outside this classification.

Problems are marked with some symbols according to following classification.

  1. Widely known and must for first timers : \(\ddagger\)
  2. Problems on Interesting connections with other areas of Physics : \(\bigstar\)
  3. Requiring numerical estiamtes and/or comparison with experiments : \(\mathfrak{N}\)
  4. Recommended for experts : \(\maltese\)
    (a) contributions of  experts
    (b) selected from works of other experts
    (c) appearing here for the first time

CLICK HERE TO SEARCH FOR  \( \boxed{1} \)  \(\boxed{2}\) \(\boxed{3}\)   \(\boxed{4}\)  

 


For browsing content in this repository
use links in
BOOK:  TABLE OF CONTENTS at the top

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kapoor kapoor's picture 2 days 16 hours ago

\(\ddagger\) Problem/QM-05001 Uncertanty principle

Summary (or abstract) not available for this node.
kapoor kapoor's picture 2 days 16 hours ago

QM-05 :: RIse of Quantum Theory

This module is about old quantum theory. Problems include application of Bohr Sommerfeld Quantization rule, uncertainty principle, useful ideas and important developments before birth of quantum mechanics.

kapoor kapoor's picture 2 days 19 hours ago

Question/QFT-15005


The interaction Hamiltonian for pion decay \(\pi^-\longrightarrow e^- +
\bar{\nu} \) can be written as \[\Hsc_\text{int} = \frac{g}{\sqrt{2}}\bar{\psi}_e(x)\gamma_\mu(1-\gamma_5)\psi(x)_\nu \partial^\mu \phi_\pi^-(x) + h.c. \]

  1. Show that the decay rate is given by \[\Gamma = \frac{g^2}{8\pi} \frac{m_e^2(m_\pi^2-m_e^2)^2}{m_\pi^3}.\]
  2. Assuming that the coupling constant for \(\pi^-\longrightarrow \mu^- +\bar{\nu} \) is equal to that for the electron decay, calculate the branching ratio \[\frac{\Gamma(\pi^-\longrightarrow \mu^- +\bar{\nu})} {\Gamma((\pi^-\longrightarrow e^- + \bar{\nu})} \]
kapoor kapoor's picture 3 days 3 hours ago

QFT/15004

{The original four fermion interaction for beta decay of  neutron
 \[n \longrightarrow p + e^- + \bar{\nu} \]
 is of the of form
 \[ \bar{\psi}_p(x)\gamma_\mu\psi_n(x) \bar{\psi}_\nu(x) \gamma^\mu \psi_e(x) +  h.c.\]
Now consider other processes given below. Which of these processes (real or virtual) are permitted and which ones are not permitted by the above interaction in the first order?

  1.   \( \bar{p} \longrightarrow \bar{n} + e^-  +\bar{\nu} \);
  2.   \( \bar{p} \longrightarrow \bar{n} + e^-  +\nu \);
  3.   \( n \longrightarrow p + e^+  + \nu \);
  4.   \( p \longrightarrow n + e^+  + \bar{\nu} \);
  5.   \( \bar{n} \longrightarrow \bar{p} + e^+  + \nu \);
  6.   \( \bar{n} \longrightarrow \bar{p} + e^+  + \bar{\nu} \).


Give brief reason in each case.

kapoor kapoor's picture 3 days 3 hours ago

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