Optionals IAS Mains Physics: Questions 34 - 39 of 307

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Question 34

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Appeared in Year: 2011 (IFS)

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Short Answer▾

Write down the expression for the Bose – Einstein distribution function and explain the meaning of the symbols used. (Section - B)

Question 35

Appeared in Year: 2002

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Essay▾

Calculate the electric field for a point on the axis of a charged ring having charge ‘q’ and Radius a show that the maximum value occur at . (20 Marks)

Explanation

Consider a circular loop of wire of negligible thickness, radius a and centre O held perpendicular to the plane of the paper. Let the loop carry a total charge + q distributed uniformly over its circumference. We have to determine electric field intensity at on axis of the loop, where .

Consider a small element AB of the loop. Let length of element…

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Question 36

Appeared in Year: 2011

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Essay▾

Solve the Schrodinger equation for a particle of mass m in an infinite rectangular well defined by the potential

Obtain the normalized Eigen function and the corresponding Eigen values. (25 Marks)

Explanation

The One-Dimensional Time Independent Schrodinger Equation
  • The one-dimensional time independent Schrodinger equation of the particle inside the well where , is

    … eq. (1)

  • As the potential energy is infinite outside the well, i.e. for , the probability of finding the particle outside the well is zero. Therefore any wave function should vanish outside …

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Question 37

Appeared in Year: 2015

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Essay▾

Show that the moment of inertia of a circular disc of mass M and radius R about an axis passing through its centre and perpendicular to its plane is . (15 Marks)

Explanation

  • Consider a circular disc of mass ‘M’ and radius ‘R’ . Let us take an axis AB perpendicular to the plane of the disc and passing through center, about which moment of inertia is to be determined. Let us divide the disc into large number of elementary concentric circular rings. Consider any one of such ring of radius and thickness .
  • Here, mass of the…

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Question 38

The Spin Half Problem and Properties of Pauli Spin Matrices
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Appeared in Year: 2003

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Short Answer▾

Show that the Pauli Matrices anti commute. (5 marks)

Question 39

Entropy, Isothermal, Adiabatic, Isobaric, Isochoric Processes and Entropy Change

Appeared in Year: 2002

Describe in Detail

Essay▾

Describe Carnot cycle and show that efficiency is given by

Where the symbols have their usual meaning. (20 Marks)

Explanation

  • The Carnot cycle is accomplished in four steps and the changes of the temperature and the entropy of the auxiliary system are plotted for each of these steps in figure 1.
  • The Carnot cycle is a thermodynamic cycle that gives the best efficiency possible. Given an amount of energy in form of heat, the Carnot cycle transforms heat put in to produce use…

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