# Charge of an Electron

Electron Charge is a fixed quantity having the value of
$e = -1.602 \times 10^{-19} C$
or, alternatively, the number of electrons required to have a combined total charge of 1 Coulomb is  $6.24 \times 10^{18}$  electrons

## Units and Dimensions of the Charge

Unit = -1 e, A.s
Dimension: $\left[ IT \right]$

## Principle of Conservation of Charges

Electric Charge of a system is conserved: Electric charge can neither be created nor be destroyed, but it can be transferred from one part of a system to another part. The total charge of an isolated system is constant. This principle is applicable universally.

## Coulomb’s Law of Electrostatic force between two charges

The Coulomb’s law states that two point charges attract or repel (depending on the fact that they are like or unlike), such that the force between them is (a) directly proportional to the product of the magnitude of two charges, and (b) inversely, proportional to the square of distance between them. In other words, the Electrostatic Force follows the Inverse-Square-Law

Mathematically,
$F = \left( \frac {1} {4 \pi \epsilon_0}\right) \left( \frac {q_1 . q_2}{r^2} \right)$

When electron charge rotates in an orbit around positive nucleus, it creates a magnetic dipole moment. In vector form,
$\vec {M_0} = - \frac {e}{2 m_e} \vec {L_0}$

The ratio of magnetic dipole moment with angular momentum of a revolving electron is called Gyromagnetic Ratio.
Gyromagnetic Ratio = $\frac {\vec {M_0}}{\vec {L_0}} = \frac {e}{2 m_e} = constant$

The value is $8.8 \times 10^{10} C/kg$

J. J. Thomson conducted an experiment to determine the specific charge of an electron (e/m). He obtained the experimental value of specific charge of electron – e/m ratio equal to $\frac {e}{m} = 1.7 \times 10^{11} C/kg$
Gyromagnetic Ratio, as calculated, is very near to the experiment value of (e/m) obtained by J. J. Thomson!