State any four uses of Van de Graaff generator. In a parallel plate air capacitor, intensity of electric field

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Q. State any four uses of Van de Graaff generator. In a parallel plate air capacitor, intensity of electric field is changing at the rate of 2\times10¹¹ V/ms. If area of each plate is 20 cm², calculate the displacement current.

Maharashtra MsbshseMaharashtra HSC (MSBSHSE) Board 2025Subjective· 4mImportance★★★★★

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The Van de Graaff generator's main use is producing very high, steady potentials for particle acceleration and related applications; displacement current follows from Maxwell's extension of Ampere's law.

Uses of a Van de Graaff generator (any four):

To accelerate charged particles (protons, ions) to very high energies for nuclear and particle-physics experiments.
To generate high-energy X-rays for medical diagnosis/therapy and industrial radiography.
To sterilise food and medical/surgical equipment using high-energy electron beams.
For research in materials science (e.g. ion implantation) and to study nuclear reactions requiring high bombarding energies.

Displacement current: Maxwell showed that a time-varying electric field between the plates of a capacitor acts as a source of magnetic field just like a conduction current, called the displacement current:

$I_d = \varepsilon_0 A\dfrac{dE}{dt}$

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2023Set F1 markMCQ
$Q. Van de Graaff generator is an electrostatic machine which produces (A) Only high current (B) Only high voltage (C) High current and high voltage (D) Low current and low voltage$
›Reveal solutionSolution

A Van de Graaff generator produces very high voltages (of the order of millions of volts) but only small currents.

In a Van de Graaff generator, charge is carried by a moving belt to a large hollow metal sphere, where it accumulates on the outer surface. Because the sphere is a conductor, added charge spreads over its surface and its potential keeps rising, reaching very high values (up …

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CBSE 2018Set ANNUAL1 markMCQ
$Q. Van de Graaff generator consists of a hollow metal sphere of diameter 2 m. If the potential on the surface of the sphere is 6 million volt, the charge accumulated over the surface of the sphere is :$
(a) 0.66 milli coulomb
(b) 1 coulomb
(c) 8.854 micro coulomb
(d) 0.33 micro coulomb
›Reveal solutionSolution

The charge accumulated on the Van de Graaff sphere works out to about 0.66 millicoulomb.

A charged conducting sphere of radius $R$ carrying charge $Q$ has a surface potential $V = \dfrac{1}{4\pi\varepsilon_0}\dfrac{Q}{R} = \dfrac{kQ}{R}$ , where $k = 9\times10^9\ N\,m^2\,C^{-2}$ .

Given: diameter $=2\,m \Rightarrow R = 1\,m$ ; $V = 6\times10^6\,V$ .

$Q = \dfrac{VR}{k} = \dfrac{(6\times10^6)(1)}{9\times10^9} = 6.67\times10^{-4}\,C = 0.667\ \text{milli coulomb} \approx 0.66\ \text{milli coulomb}$

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Q.State any four uses of Van de Graaff generator. In a parallel plate air capacitor, intensity of electric field is changing at the rate of 2×10¹¹ V/ms. If area of each plate is 20 cm², calculate the displacement current.

Concept understanding — Van de Graaff Generator

Q.State any four uses of Van de Graaff generator. In a parallel plate air capacitor, intensity of electric field is changing at the rate of 2×10¹¹ V/ms. If area of each plate is 20 cm², calculate the displacement current.

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