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