Q. 4 A4.4( 120 Votes )
Explain the meaning of the statement ‘electric charge of a body is quantised’.
Electric charge of a body is quantised.
This statement means that charge on a body can take only integral values i.e. (1, 2, 3, 4, …. N) number of electrons can be transferred from one body to another. The charges cannot be transferred in fractions. It can only be an integral multiple of the charge of one electron.
Therefore, as a result, a body will possess a charge that is an integral multiple of the electric charge of an electron.
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There is another useful system of units, besides the SI/mksA system, called the cgs (centimeter-gram-second) system. In this system Coloumb’s law is given by Frr =
where the distance r is measured in cm (= 10–2 m), F in dynes (=10–5 N) and the charges in electrostatic units (es units), where 1es unit of charge 9 1 10 C  − = ×
The number  actually arises from the speed of light in vaccum which is now taken to be exactly given by c = 2.99792458 × 108 m/s. An approximate value of c then is c =  × 108 m/s.
(i) Show that the coloumb law in cgs units yields
1 esu of charge = 1 (dyne)1/2 cm.
Obtain the dimensions of units of charge in terms of mass M, length L and time T. Show that it is given in terms of fractional powers of M and L.
(ii) Write 1 esu of charge = x C, where x is a dimensionless number. Show that this gives
9 2 2 2 0 1 10 N.m 4x C π − = ∈
With , we have 9 1 x 10  − = ×
2 2 9 2 0 1 Nm  10 4C π = × ∈
Or, (exactly) 2 2 9 2 0 1 Nm [2.99792458] 10 4C π = × ∈
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charges q and –3q are placed fixed on x-axis separated by distance ‘d’. Where should a third charge 2q be placed such that it will not experience any force?Physics - Exemplar
Two particles A and B, each carrying a charge Q, are held fixed with a separation d between them. A particle C having mass m and charge q is kept at the middle point of the line AB.
(a) If it is displaced through a distance x perpendicular to AB, what would be the electric force experienced by it.
(b) Assuming x << d, show that this force is proportional to x.
(c) Under what conditions will the particle C execute simple harmonic motion if it is released after such a small displacement?
Find the time period of the oscillations if these conditions are satisfied.
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