Electric Charges and Fields

Ans.1.5 When two bodies are rubbed against each other, it produces charges of equal magnitude in both the bodies but of opposite in nature. Hence the net charges of the two bodies are zero. When a glass rod is rubbed with a silk cloth, similar phenomena occur. This is as per the law of conservation of energy.

1.4 

(a) Electric charge of a body is quantized, this means that only integers (1,2,3, ….n) number of electrons can be transferred from one body to the other. Charges are not transferred in fraction. Hence, a body possesses total charge only in integers.

(b) In macroscopic i.e. large scale charges, the charges used are huge as compared to the electric charge of electrons or protons. Therefore, it is ignored and it is considered that electric charge is continuous.

1.3 The units of the given equation 

$\frac{{ke}^2}{G{m}_e{m}_p}$ is

e = Electric charge in C

k = $\frac{1}{4\pi {?}_0}$ in N $m^2{C}^{-2},$ where ${?}_0$ = Permittivity of free space = 8.854 $*{10}^{-12}$ $C^2{N}^{-1}$ $m^{-2}$

G = Gravitational constant = N $$

$m^2{kg}^{-2}$

${\mathrm{m}}_{\mathrm{e}}=\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{}\mathrm{o}\mathrm{f}\mathrm{}\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{o}\mathrm{n}\mathrm{}\mathrm{i}\mathrm{n}\mathrm{}\mathrm{k}\mathrm{g},\mathrm{}\mathrm{}{\mathrm{m}}_{\mathrm{p}}=\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{}\mathrm{o}\mathrm{f}\mathrm{}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{t}\mathrm{o}\mathrm{n}\mathrm{}\mathrm{i}\mathrm{n}\mathrm{}\mathrm{k}\mathrm{g}$

Therefore

$\frac{{ke}^2}{G{m}_e{m}_p}$ = $\frac{\left[\mathrm{N}{m}^2{C}^{-2}\right]*\left[C^2\right]}{\left[\mathrm{N}{m}^2{kg}^{-2}\right]\left[kg\right]\left[kg\right]}$= $M^0{L}^0{T}^0$

So the given equation is dimensionless

We have the following values

e = 1.6 $*{10}^{-19}$ C

G = 6.67  $*{10}^{-11}$${\mathrm{Nm}}^2{kg}^{-2}$ kg

${\mathrm{m}}_{\mathrm{e}}=9.1*{10}^{-31}$ kg

${\mathrm{m}}_{\mathrm{p}}=1.66*{10}^{-27}$

The numerical value of this ratio is given by

$\frac{{ke}^2}{G{m}_e{m}_p}$ = $\frac{\left[\mathrm{N}{m}^2{C}^{-2}\right]*\left[C^2\right]}{\left[\mathrm{N}{m}^2{kg}^{-2}\right]\left[kg\right]\left[kg\right]}$ = $\frac{1}{4\pi {?}_0}$ = $*\frac{e^2}{G{m}_e{m}_p}$= 
$\frac{1}{4*\pi *8.854\mathrm{}*{10}^{-12}}$ $*\frac{{(1.6\mathrm{}*{10}^{-19})}^2}{6.67*{10}^{-11}*{9.1*{10}^{-31}*1.66*{10}^{-27}}_{}}$

 = 2.284$*{10}^{39}$

The fundamental relationship between the resulting electric field and electric charge distribution is given by Gauss's law.
It states that the total electric flux (? E) passing through any closed hypothetical surface (called a Gaussian surface) is equal to 1/?0 times the net electric charge (q enc ) enclosed within that surface.
When dealing with charge distributions that possess a high degree of symmetry such as planar, cylindrical, and spherical, Gauss's law significance lies in providing a powerful alternative method to Coulomb's law for calculating electric fields.
?

The quantization of charge can be denoted as e = 1.6 * 10? ¹? C. It means that the object's charge is an integral multiple of the elementary charge. Mathematically, it can be represented as q = ±ne, where n is an integer. The charge exists in discrete packets or quanta and is not continuous. For example, a body cannot have a charge of 2.5e but a charge of 3e or -2e. Millikan first observed this quantization of charge in his oil drop experiment. Quantization is consistent with the matter's atomic structure and is a fundamental property of electric charge.