Skip to main content

Coulomb's Law in Electrostatics | SI Unit of charge

Coulomb's Law in Electrostatics

Coulomb's law in electrostatics is the electrical analog of Newton's law of gravitation. In 1785, Coulomb measured the force of attraction or repulsion between two electrical charges by using a torsion balance. His observations are known as Coulomb's law in electrostatics.

It states that two-point charges attract or repel each other with a force that is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.

The force is repulsive if the charges are alike and attractive in case of unlike charges. Further, the electrostatic force between two charges is central in nature. It may be pointed out that Columb's law in electrostatics holds for stationary charges. Further, the two charges should be points in size. Consider that two charges q, and q2 are present at points A and B at a the distance r apart as shown in Fig. 1.03. Then, the force between the two charges, Combining the equations (1.01) and (1.02), we have

F  q1q2..............................(1.01)

 1/r^2.............................(1.02)
Combining the equations (1.01) and (1.02), we have 
F ∝ q1q2/r2
Or 
F=k(q1q2/r2)

where k is the constant of proportionality. Its value depends upon the nature of the medium in which the two charges are located and also the system of units adopted to measure F, q1,q2 and r. In SI, when the two charges are located in a vacuum or air,

k=1/4π€

where E, is called the absolute permittivity of free space. Therefore, from equation (1.03), the force between two charges located in air or vacuum  given by

Fvac= 1/4π€. q1q2/r2

The absolute permittivity of free space is measured to be 
€=8.854 x 10-12 C² N-1 m-² 

= 1/4π8.854 x 10-12 C² N-1 m-² . 

=9x10⁹ Nm² C-2

 Hence, the equation (1.04) may be written as

Fvac = 9 x 10^9 x q1q2/r^2 (in newton)........(1.05)

SI Unit of charge

In SI, the force between two charges ₁ and 2 held at a distance r apart in a vacuum is given by

 F= 9 × 10⁹ × 2^9 x q₁ q₂/r^2

Suppose that q₁ q₂ = q (say); r = 1 m and Fie = 9 × 10⁹ N

Then,

9 × 10⁹=9 × 10⁹ q₁ q₂/r^2
or

q² =1 
q= + or  - 1 coulomb (C)

Therefore, one coulomb is a charge which repels an equal and similar charge with a force of 9×10° N, when placed in a vacuum (or air) at a distance of one meter from it.

Note. 1. In an electrostatic cgs system, the unit of charge is known as the electrostatic unit of charge (e.s.u. of charge). It is also called statcoulomb (stat C)

1 C=3 x 10⁹ stat C

2. In an electromagnetic cgs system, the unit of charge is known as the electromagnetic unit of charge (e.m.u. of charge).

1 1C=  1/10 e.m.u. of charge



Comments

Popular posts from this blog

An Elementary School Classroom in a Slum Explanation Stanza by Stanza

An Elementary School Classroom In a Slum Detailed Explanation Stanza by Stanza --Stephen Spender Stanza 1 Far far gusty waves these children's faces. Like rootless weeds, the hair torn around their pallor : The tall girl with her weighed-down head. The paper- seeming boy, with rat's eyes. The stunted, unlikely heir Of twisted bones, reciting a after's gnarled disease, His lesson, from his desk. At back of the dim class One unnoted , sweet and young. His eyes live in a dream, Of squirrel's game, in tree room, other than this. Explanation: The poet sees children sitting in the classroom of a school in a slum. He describes their sad and pathetic looks through moving words-pictures. He says that the bloodless faces of these children are far from the gusty waves of life and activity that are a mark of childhood. Their untidy hair hanging around their white pale faces looks like rootless weeds. There is a tall girl with her head weighed down. A pale-looking boy sitting agai