GATE PH exam:gate PYQs & Answers — Page 49

Questions 481–490 of 650. Imported answers require independent review unless marked reviewed.

Topic practice 650 questionsPage 49 of 65

An infinitely long thin cylindrical shell has its axis coinciding with the

-axis. It carries a surface charge density

, where

is the polar angle and

is a constant. The magnitude of the electric field inside the cylinder is

Your answerChoose one option.

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Consider a three-dimensional crystal of

inert gas atoms. The total energy is given by

, where

, and

is the nearest neighbor distance between two atoms. The two constants,

and

, have the dimensions of energy and length, respectively. The equilibrium separation between two nearest neighbor atoms in units of

(rounded off to two decimal places) is

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The energy-vector (

) dispersion relation for a particle in two dimensions is

, where

is a constant. If its density of states

is proportional to

then the value of

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A circular loop made of a thin wire has radius 2 cm and resistance 2

. It is placed perpendicular to a uniform magnetic field of magnitude

Tesla. At time

the field starts decaying as

, where

s. The total charge that passes through a cross section of the wire during the decay is

. The value of

C (rounded off to two decimal places) is

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The electric field of an electromagnetic wave in vacuum is given by

The wave is reflected from the

surface. If the pressure exerted on the surface is

, the value of

(rounded off to one decimal place) is

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The Hamiltonian for a quantum harmonic oscillator of mass

in three dimensions is

where

is the angular frequency. The expectation value of

in the first excited state of the oscillator in units of

(rounded off to one decimal place) is

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The Hamiltonian for a particle of mass

where

and

are the generalized coordinate and momentum, respectively,

is time and

is a constant. For the initial condition,

and

. The value of

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At temperature

Kelvin (K), the value of the Fermi function at an energy 0.5 eV above the Fermi energy is 0.01. Then,

, to the nearest integer, is

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Let

represent two possible states of a two-level quantum system. The state obtained by the incoherent superposition of

and

is given by a density matrix that is defined as

. If

and

, the matrix element

(rounded off to one decimal place) is

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A conventional type-I superconductor has a critical temperature of 4.7 K at zero magnetic field and a critical magnetic field of 0.3 Tesla at 0 K. The critical field in Tesla at 2 K (rounded off to three decimal places) is

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