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Units and Measurements

Section: Physics

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Question : 33 of 36

Marks: +1, -0

A dense collection of equal number of electrons and positive ions is called neutral plasma. Certain solids containing fixed positive ions surrounded by free electrons can be treated as neutral plasma. Let N be the number density of free electrons, each of mass m. When the electrons are subjected to an electric field, they are displaced relatively away from the heavy positive ions. If the electric field becomes zero, the electrons begin to oscillate about the positive ions with a natural angular frequency

ω_p

which is called the plasma frequency. To sustain the oscillations, a time varying electric field needs to be applied that has an angular frequency ω, where a part of the energy is absorbed and a part of it is reflected. As ω approaches

ω_p

all the free electrons are set to resonance together and all the energy is reflected. This is the explanation of high reflectivity of metals.

Taking the electronic charge as e and the permittivity as

ε_0

. Use dimensional analysis to determine the correct expression for

ω_p

[JEE Adv 2011 P1]

$\frac{N_e}{m\varepsilon_0}$
$\sqrt{\frac{m\varepsilon_0}{Ne}}$
$\sqrt{\frac{Ne^{}}{m\varepsilon_0}}$
$\sqrt{\frac{m\varepsilon_0}{Ne^2}}$

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