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The document provides a sample syllabus and questions for the entrance test for the Ph.D. Programme at the Tata Institute of Fundamental Research. The syllabus covers areas like classical mechanics, mathematics relevant to physics, electricity and magnetism, quantum mechanics, thermodynamics, statistical physics, general physics, modern physics, and experimental physics. Four multiple choice sample questions are provided covering complex analysis, particle motion in electric and magnetic fields, electron transitions in hydrogen atoms, and particle distribution in energy levels.
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![Tata Institute of Fundamental Research
Entrance test for the Ph.D. Programme: Sample Questions
PHYSICAL SCIENCES
SYLLABUS
In general, the syllabus for the Admissions Tests in Physics (Written and Interview)
is typically a course of studies in Physics as the main subject in the Undergraduate
and Masters levels in an Indian University. The questions in the written test (multiple-
choice type) and the interviews are distributed over the following areas: Classical
Mechanics; Mathematics relevant to Physics; Electricity and Magnetism; Quantum
Mechanics; Heat, Thermodynamics and Statistical Physics; General Physics;
Modern Physics; Electronics and Experimental Physics.
SAMPLE QUESTIONS
(NOTE: Wrong answers will get you negative marks)
1. The function f(z) = z2
+ 1 is integrated over a circle of unit radius in the complex z
plane. What is the value of the integral?
[a] 1 [b] i [c] 0
2. Charged particles are beamed into a region having a uniform electric field of 103
Newton/Coulomb and a uniform magnetic field of 10-2
Newton/(ampere meter). The
electric and magnetic fields are at right angles to each other and the beam of
particles is directed perpendicular to both of them, so that the electrical and magnetic
forces on an ion oppose each other. The speed of those ions that are unaffected
through this region is:
[a] 104
m/s [b] 105
m/s [c] 106
m/s](https://image.slidesharecdn.com/51616c10-38ca-4040-b07e-2b923c760a86-150220215654-conversion-gate01/85/Paper_Physics-1-320.jpg)
![3. The electron in a free Hydrogen atom is initially in the state with quantum
numbers n = 3 and 1 = 2. It makes an electric dipole transition to a lower energy
state. Which of the given states could it finally be in?
[a] n = 3, 1 = 0 [b] n = 2, 1 = 2 [c] n = 2, 1 = 1
4. N particles are distributed amongst three levels having energies 0, kT and 2kT. If
the total equilibrium energy of the system is approximately 425kT, what is the value
of N?
[a] 1001 [b] 335 [c] 425 [d] 390 [e] 181](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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The chapter gives brief knowledge about formation of bands in solids. What are free electrons how they contribute for conductivity in conductors, but can be extended to semiconductors also.
Drude Model-Dielectric constant of metals
This document discusses the Drude model for explaining the optical and electric properties of metals using a free electron gas model. It describes how the Drude model relates the dielectric constant of metals to oscillations of free electrons in response to an applied electromagnetic field. It defines key terms like plasma frequency, damping frequency, and presents equations for the real and imaginary components of the dielectric function and how they describe polarization and energy dissipation in metals. Graphs are shown depicting how the real part of permittivity is negative at lower frequencies but becomes zero near the plasma frequency.
NEET 2022 (1).pdf
Download the previous year NEET question paper with the answer key for the years 2022–2023 only on Zephyr.
https://zephyrentrance.in/neet-quiestion-papers
Ajal electrostatics slides
Since classical physics, it has been known that some materials, such as amber, attract lightweight particles after rubbing. The Greek word for amber, ήλεκτρον, or electron, was the source of the word 'electricity'. Electrostatic phenomena arise from the forces that electric charges exert on each other. Such forces are described by Coulomb's law. Even though electrostatically induced forces seem to be rather weak, some electrostatic forces such as the one between an electron and a proton, that together make up a hydrogen atom, is about 36 orders of magnitude stronger than the gravitational force acting between them.
There are many examples of electrostatic phenomena, from those as simple as the attraction of the plastic wrap to one's hand after it is removed from a package to the apparently spontaneous explosion of grain silos, the damage of electronic components during manufacturing, and photocopier & laser printer operation. Electrostatics involves the buildup of charge on the surface of objects due to contact with other surfaces. Although charge exchange happens whenever any two surfaces contact and separate, the effects of charge exchange are usually only noticed when at least one of the surfaces has a high resistance to electrical flow. This is because the charges that transfer are trapped there for a time long enough for their effects to be observed. These charges then remain on the object until they either bleed off to ground or are quickly neutralized by a discharge: e.g., the familiar phenomenon of a static "shock" is caused by the neutralization of charge built up in the body from contact with insulated surfaces.
Electrical Charges and Coulomb's Law.pptx
1) The document discusses electrical charges and Coulomb's law. It defines electric charge, the two types of charges (positive and negative), and how like charges repel and unlike charges attract based on Coulomb's law.
2) Coulomb's law gives the formula for the magnitude of the electrostatic force between two point charges, defining it as directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
3) Several examples show how to calculate the electrostatic force between charges using Coulomb's law and solving for unknown distances or forces.
1.1 electric charge
- Coulomb's law describes the electric force between two point charges. It states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
- The document discusses various methods of charging objects, including rubbing, conduction, and induction. It also describes the properties of conductors and insulators.
- Examples are provided to demonstrate how to use Coulomb's law to calculate the electric force between charges, including resolving forces into components. Equilibrium situations involving electric forces and other forces are also analyzed.
Plasma Chemistry CH2
This document summarizes key concepts in plasma chemistry from Chapter 2 of the reference book, including:
1) Elementary plasma reactions are determined by micro-kinetic characteristics like cross-sections and reaction probabilities, as well as kinetic distribution functions.
2) Collisions can be elastic, inelastic, or superelastic depending on whether the total kinetic energy and internal energies change during the collision.
3) Ionization processes include direct electron impact ionization, stepwise ionization, ion-molecule collisions, photoionization, and surface ionization.
4) The Thomson formula describes direct electron impact ionization cross-sections at high energies, while the Frank-Condon principle applies to ionization
Plasma Chemistry CH2_part2
Elementary plasma-chemical reactions can be described by micro-kinetic characteristics like cross-sections and reaction probabilities. There are several types of ionization processes including direct electron impact ionization, stepwise ionization, and ionization by photons or heavy particles. Collision parameters include the cross-section, probability, mean free path, and reaction rates. Direct ionization follows the Thomson formula at high energies. Molecular ionization is affected by the Frank-Condon principle where atomic positions remain fixed. Stepwise ionization occurs through excitation to an energy above the ionization potential. High-energy electrons like in beams follow the Bethe-Bloch formula for energy loss per unit length.
lecture classical and Quantum Free electron theory (FERMI GAS) (23-24).pdf
The electron theory of solids explains properties through electronic structure. It applies to metals and nonmetals. The theory developed in three stages:
1. Classical free electron theory treated electrons as free gas particles. It could not explain many properties.
2. Quantum free electron theory incorporated quantum mechanics. Electrons occupy discrete energy levels according to Fermi-Dirac statistics.
3. Band theory views electrons moving in periodic potentials of atom arrays. It explains conductivity, effective mass, and the origin of band gaps.
EMWT_UNIT 1_DIELECTRICS.pptx
1. Dielectric materials are insulators in which electrons are tightly bound and there is no free charge. They can be classified as active or passive.
2. Active dielectrics readily store electrical energy, like piezoelectric and ferroelectric materials. Passive dielectrics restrict electrical flow and act as insulators, like glass and rubber.
3. When dielectric materials are placed in an electric field, dipoles are induced through mechanisms like electronic, ionic, orientational and space charge polarization, contributing to the material's dielectric properties. The different polarization mechanisms have varying frequency dependencies.
Chapter_6.pptx .
This document discusses molecular bonding, energy states of molecules, bonding in solids, and electrical properties of materials. It begins by explaining different types of molecular bonding mechanisms including ionic, covalent, van der Waals, and hydrogen bonding. It then discusses the energy states and spectra of molecules, including rotational, vibrational, and electronic transitions. The document next summarizes bonding in ionic solids, covalent solids, and metallic solids. It concludes by covering electrical conduction in metals, insulators, and semiconductors, as well as properties and applications of superconductivity.
Dielectrics
Dielectrics are materials that have permanent electric dipole moments. They contain atoms or molecules with separated positive and negative charges even in the absence of an electric field. When a dielectric is placed in an electric field, the electric dipoles within align with the field, causing polarization. There are several types of polarization that can occur in dielectrics, including electronic, ionic, and orientational polarization, each occurring at different frequencies. The dielectric constant of a material is a measure of how much it increases the electric flux density compared to empty space.
Apartes de la Conferencia de la SJG del 14 y 21 de Enero de 2012Nonlinear ele...
Apartes de la Conferencia de la SJG del 14 y 21 de Enero de 2012Nonlinear ele...SOCIEDAD JULIO GARAVITO
This document summarizes a research article about nonlinear electrodynamics and its effects on the polarization of the cosmic microwave background radiation. It introduces nonlinear electrodynamics models as alternatives to Maxwell's electrodynamics. The document then discusses how nonlinear electrodynamics is minimally coupled to gravity and derives the relevant equations of motion. It focuses on analyzing the Pagels-Tomboulis nonlinear electrodynamics Lagrangian and computing the polarization angle of photons propagating in an expanding universe with planar symmetry. Constraints on the nonlinear electrodynamics parameter are obtained using data on cosmic magnetic field strengths and the rotation of CMB polarization spectra measured by experiments.Electronicdevicescircuits 140517065905-phpapp01
This document provides an overview of semiconductor theory and electronic devices and circuits. It discusses atomic structure, energy band theory, insulators, semiconductors and metals. It describes charge densities in semiconductors, the Fermi level, drift and diffusion currents, and the Hall effect. It also includes sample assignments and analysis of past GATE exam questions related to electronic devices.
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Paper_Physics
- 1. Tata Institute of Fundamental Research Entrance test for the Ph.D. Programme: Sample Questions PHYSICAL SCIENCES SYLLABUS In general, the syllabus for the Admissions Tests in Physics (Written and Interview) is typically a course of studies in Physics as the main subject in the Undergraduate and Masters levels in an Indian University. The questions in the written test (multiple- choice type) and the interviews are distributed over the following areas: Classical Mechanics; Mathematics relevant to Physics; Electricity and Magnetism; Quantum Mechanics; Heat, Thermodynamics and Statistical Physics; General Physics; Modern Physics; Electronics and Experimental Physics. SAMPLE QUESTIONS (NOTE: Wrong answers will get you negative marks) 1. The function f(z) = z2 + 1 is integrated over a circle of unit radius in the complex z plane. What is the value of the integral? [a] 1 [b] i [c] 0 2. Charged particles are beamed into a region having a uniform electric field of 103 Newton/Coulomb and a uniform magnetic field of 10-2 Newton/(ampere meter). The electric and magnetic fields are at right angles to each other and the beam of particles is directed perpendicular to both of them, so that the electrical and magnetic forces on an ion oppose each other. The speed of those ions that are unaffected through this region is: [a] 104 m/s [b] 105 m/s [c] 106 m/s
- 2. 3. The electron in a free Hydrogen atom is initially in the state with quantum numbers n = 3 and 1 = 2. It makes an electric dipole transition to a lower energy state. Which of the given states could it finally be in? [a] n = 3, 1 = 0 [b] n = 2, 1 = 2 [c] n = 2, 1 = 1 4. N particles are distributed amongst three levels having energies 0, kT and 2kT. If the total equilibrium energy of the system is approximately 425kT, what is the value of N? [a] 1001 [b] 335 [c] 425 [d] 390 [e] 181