Electric Field And Charges

Introduction

All of us have the experience of seeing a spark or hearing a crackle when we take off our synthetic clothes or sweater, particularly in dry weather. The reason for this is discharge of electric charges through our body, which were accumulated due to rubbing of insulating surfaces. Electrostatics deals with the study of forces, fields and potentials arising from static charges.

Electric Charge

It was concluded, after many careful studies by different scientists, that there were only two kinds of an entity which is called the Electric Charge. And the charges were named as positive and negative by the American scientist Benjamin Franklin.

Conductors and Insulators

Some substances readily allow the passage of electricity through them others do not. Those which allow electricity to pass through them easily are called Conductors. They have electric charges (electrons) that are comparatively free to move inside the material. Metals, Human and Animal bodies and Earth are conductors. Most of the non-metals like glass, porcelain, plastic, nylon, wood offer high resistance to the passage of electricity through them. They are called Insulators.

Quantisation of Charge

Experimentally it is established that all free charges are integral multiple of basic unit of charge denoted by e. Thus charge q on a body is always given by 

q=ne

where n is any integer, positive or negative. This basic unit of charge is the charge that an electron or proton carries. By convention, the charge on an electron is taken as negative and on a proton it is taken as positive. The fact electric charge is always an integral multiple of e is termed as quantisation of charge.

e = 1.602192 x 10^-19 C (This is Universal Constant)

Thus, there are about 6 x 10^18 electrons in a charge of -1C.

Coulomb's Law

Coulomb's law is a quantitative statement about the force between two point charges. Coulomb measured the force between two point charges and found that it varied inversely as the square of the distance between the charges and directly proportional to the product of the magnitude of the two charges and acted along the line joining the two charges. Thus, if two point charges q1, q2 are seperated by a distance of r in vaccum, the magnitude of the force (F) between them is given by

F = k|q1.q2|/r^2       Eq[1]

Here k = constant, and it's value is k = 9 x 10^9N.

It is also the force of attraction or repulsion between two unit charges seperated by the distance r = 1.

The constant k in equation [1] is usually put as k = 1/4πε0       Eq[2]

ε0 is called the permittivity of free space. The value of ε0 in SI units is

 ε0 = 8.854 x 10^-12 C^2N^-1m^-2

 Force is a vector it is better to right coulomb's law in the vector notation. Let the position vector of charges q1 and q2 be r1 and r2 respectively. See figure

We denote force on q1 due to q2 as F12 and force on q2 due to q1 as F21. The two point charges q1 and q2 have been numbered one and two for convenience and the vector leading from 1 to 2 is denoted by r21 and vice versa: 

r21 = r2 - r1

r12 = r1 - r2

Coulomb's force law between two point charges q1 and q2 located at r1 and r2 is then expressed as

F21 = 1/4πε0 x q1.q2/r21^2 x r21(cap)

Here r21(cap) is a unit vector along the direction of r21.

And by sign convention F12 = -F21.