GATE Physics: Questions 64 - 68 of 290

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Question number: 64

» Electromagnetic Theory » Solutions of Electrostatic and Magnetostatic Problems

Appeared in Year: 2016

Short Answer Question▾

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The magnitude of the magnetic dipole moment associate with a square shaped loop carrying a steady current I is m . If this loop is changed to a circular shape with the same current I passing it, the magnetic moment becomes pmπ . The value of p is _ .

Question number: 65

» Quantum Mechanics » Linear Vectors and Operators in Hilbert Space

Appeared in Year: 2016

MCQ▾

Question

Which of the following operators is Hermitian?

Choices

Choice (4) Response

a.

id2dx2

b.

ddx

c.

d3dx3

d.

d2dx2

Question number: 66

» Classical Mechanics » Small Oscillations and Normal Modes

Appeared in Year: 2014

Short Answer Question▾

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At a given temperature, T, the average energy per particle of a non – interacting gas of two – dimensional classical harmonic oscillators is ________ kBT .

( kB is the Boltzmann constant).

Question number: 67

» Thermodynamics and Statistical Physics » Free Energy

Appeared in Year: 2016

MCQ▾

Question

For a system at constant temperature and volume, which of the following statements is correct at equilibrium?

Choices

Choice (4) Response

a.

The Gibbs free energy attains a local minimum.

b.

The Helmholtz free energy attains a local minimum.

c.

The Helmholtz free energy attains a local maximum.

d.

The Gibbs free energy attains a local maximum.

Question number: 68

» Solid State Physics » Lattice Vibrations and Thermal Properties of Solid

Appeared in Year: 2015

Short Answer Question▾

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The dispersion relation for phonons in a one dimensional monatomic Bravais lattice with lattice spacing a and consisting of ions of masses M is given by,

ω(k)=2CM[1cos(ka)]

Where ω is the frequency of oscillation, k is the wavevector and C is the spring constant. For the long wavelength modes (λa) , the ratio of the phase velocity to the group velocity is ________.

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