Q. 24.3( 134 Votes )
The electrostatic force on a small sphere of charge 0.4 μC due to another small sphere of charge –0.8 μC in air is 0.2 N.
(a) What is the distance between the two spheres? (b) What is the force on the second sphere due to the first?
(a) The electrostatic force, F = 0.2 N
Charge on this present sphere, q1 = 0.4 μC = 0.4 × 10-6 C
Charge on the other sphere, q2 = –0.8 μC = -0.8 × 10-6 C
The electrostatic force between the spheres can be given by the equation,
Where, q1 and q2 are the charges.
r is the distance between the charges.
is a constant and its value is 9x109 N m2 C-2
ϵ0 is the permittivity of free space. Its value is 8.85 x 10-12 (F/m)
Therefore, from equation (1),
⇒ r2 = 144 x 10-4 m2
Taking square root both the sides,
⇒ r =
r = 0.12 m
Hence, the distance between the two spheres is 0.12 m.
(b) Since the nature of the charges on the spheres is opposite, the force between them will be attractive in nature. The spheres will attract each other with the same amount of force.
Therefore, the force on the second sphere due to the first sphere will be 0.2 N.
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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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