Smallest charge that can exist in nature is the charge of an electron. During friction it is only the transfer of electrons which makes the body charged. Hence net charge on any body is an integral multiple of charge of an electron.

[1.6 x 10^-19 C] i.e.                                  
q = ± ne
where n = 1,2,3,4, ....
Hence no body can have a charge represented as \(1.1 e, 2.7 e, \frac{3}{5} e, \text { etc. }\)
Recently, it has been discovered that elementary particles such as protons or neutrons are composed of more elemental units called quarks.
(i) Which of the following properties is not satisfied by an electric charge?

(ii) Which one of the following charges is possible?

(iii) If a charge on a body is 1 nC, then how many electrons are present on the body?

(iv) If a body gives out 10⁹ electrons every second, how much time is required to get a total charge of 1 C from it?

(v) A polythene piece rubbed with wool is found to have a negative charge of3.2 x 1O^-7C.Calculate the number of electrons transferred.

In 1909, Robert Millikan was the first to find the charge of an electron in his now-famous oil-drop experiment. In that experiment, tiny oil drops were sprayed into a uniform electric field between a horizontal pair of oppositely charged plates. The drops were observed with a magnifying eyepiece, and the electric field was adjusted so that the upward force on some negatively charged oil drops was just sufficient to balance the downward force of gravity. That is, when suspended, upward force qE just equaled Mg. Millikan accurately measured the charges on many oil drops and found the values to be whole number multiples of 1.6 x 10^-19 C the charge of the electron. For this, he won the Nobel prize.

(i) If a drop of mass 1.08 x 10^-14 kg remains stationary in an electric field of 1.68 x 10⁵ N C^-I, then the charge of this drop is

(ii) Extra electrons on this particular oil drop (given the presently known charge of the electron) are

(iii) A negatively charged oil drop is prevented from falling under gravity by applying a vertical electric field 100 V m^-1.If the mass of the drop is 1.6 X 10^-3 g, the number of electrons carried by the drop is (g= 10 m s^-2)

(iv) The important conclusion given by Millikan's experiment about the charge is

(v) If in Millikan's oil drop experiment, charges on drops are found to be \(8 \mu \mathrm{C}, 12 \mu \mathrm{C}, 20 \mu \mathrm{C}\) then quanta of charge is

Electric field strength is proportional to the density of lines of force i.e., electric field strength at a point is proportional to the number of lines of force cutting a unit area element placed normal to the field at that point. As illustrated in the given figure, the electric field at P is stronger that at Q.

(i) Electric lines of force about a positive point charge are

(ii) Which of the following is false for electric lines of force?

(iii) Which one of the following pattern of electric line of force in not possible in filed due to stationary charges?

(iv) Electric lines of force are curved

(v) The figure below shows the electric field lines due to two positive charges. The magnitudes E_A, E_B and E_c of the electric fields at points A, Band C respectively are related as

In practice, we deal with charges much greater in magnitude than the charge on an electron, so we can ignore the quantum nature of charges and imagine that the charge is spread in a region in a continuous manner. Such a charge distribution is known as continuous charge distribution. There are three types of continuous charge distribution : (i) Line charge distribution (ii) Surface charge distribution (iii) Volume charge distribution as shown in figure.

(I) Statement 1 : Gauss's law can't be used to calculate electric field near an electric dipole.
Statement 2 : Electric dipole don't have symmetrical charge distribution.

(ii) An electric charge of 8.85 X 10^-13 C is placed at the centre of a sphere of radius 1 m. The electric flux through the sphere is

(iii) The electric field within the nucleus is generally observed to be linearly dependent on r. So,

(iv) What charge would be required to electrify a sphere of radius 25 cm so as to get a surface charge density of \(\frac{3}{\pi} \mathrm{C} \mathrm{m}^{-2} ?\)

(v) The SI unit of linear charge density is

Surface charge density is defined as charge per unit surface area of surface charge distribution. i.e., \(\sigma=\frac{d q}{d S}\) Two large. thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs having magnitude of 17.0 x 10^-22 C m^-2 as shown. The intensity of electric field at a point is \(E=\frac{\sigma}{\varepsilon_{0}}\) where \(\varepsilon_{0}\) = permittivity of free space.

(i) E in the outer region of the first plate is

(ii) E in the outer region of the second plate is

(iii) E between the plates is

(iv) The ratio of E from right side of B at distances 2 cm and 4 ern, respectively is

(v) In order to estimate the electric field due to a thin finite plane metal plate, the Gaussian surface considered is