coulombs law is only true for point charges whose sizes are

coulombs law is only true for point charges whose sizes are  ?

Coulomb’s Law

Coulomb’s law gives the force between two point charges. When the linear size of charged bodies are much smaller than the distance separating them, the size may be ignored and the charged bodies are considered as point charges.According to the Coulomb’s law force between the two point charges is 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.

If two point charges and  are separated by a distance rin vacuum then the magnitude of the force of repulsion or attraction between them is

Where K is proportionality constant which is depend on the medium between the charges and the value of k in vacuum is  N-m² –C^-2.

If the charges  and  are of the similar in nature (both positive and both negative) then the force is mutually repulsive and the force on each charge points away from the other charge as shown in figure (a).And if the charges are of opposite in nature (one positive, one negative) then the force is mutually attractive and the force on each charge points toward the other one as shown in figure (b).

Figure (a) Charges with same nature has repulsive force.	Figure (b) Charges with opposite nature has attraction force.

 

Permittivity:According to coulomb’s law the force between two point charges is

Where K is proportionality constant which is depend on the medium between two charges because every medium has certain characteristics like density, temperature and viscosity. Hence the value of K will change with different. When a charge trying apply force on another charge through a medium then the medium whether allow it or not allow it this characteristics is call permittivity. Hence in proper words the permittivity is an electrical characteristics of medium due to which it absorbs effect of due which force is applied on other charge. It is denoted epslon (.It is expressed in number and unit. And the relation between proportional constant and permittivity is found as  . The value of permittivity will vary medium to medium. Permittivity for vacuum or free space is  and value of it is C² N^–1m ^–2. So standard form Coulumb’s lawin free space is

Note: The value of permittivity and free space is about same.

Relative Permittivity:Again according to the coulumb’s law

 

Here  electric characteristics of medium how much it will absorb the electric force.And we assume that permittivity of free space is and absolute permittivity of given medium is .

Then the relative permittivity is the ratio of absolute permittivity to free space permittivity it is denoted by . Hence

Or

Coulumb force in vacuum in free space is

…………………… (1)

Coulumb force in given medium which has absolute permittivity

………………(2)

Dividing equation (1) by equation (2) then

By simplification

…………………………(3)

By the definition of permittivity

……………………. (4)

Or                    …………………… (5)

Hence it can be seen from equation (5) that the force in medium is times less than force in free space.The value of  for air or free space is equal to one.  And value of  for any other medium is more than one.

 Important Note:

• In S.I. System of units, the unit of charge is Coulomb.
• One coulomb is defined as that charge, which, when placed at a distance of 1 m in air or vacuum from an equal and similar charge, repel it with a force of 9 x 10⁹
• Coulomb is that quantity of charge which passes across any section of a conductor per second when current of one ampere flows through it, i.e. 1 coulomb=1 Ampere x 1 sec.
• In CGS electrostatic system, the unit of charge is called as STATECOULUMB or esu of charge.
• One stat coulomb is defined that amount of charge which when placed at a distance of 1 cm in air from an equal and similar charge repel it with a force of one dyne.
• In CGS electromagnetic system, the unit of charge is called ABCOULOMB or emu of charge

1 Coulomb = 3 x 10⁹ statcoulomb

= 1/10 abcoulomb

\ 1 emu = 3×10¹⁰ esu of charge

Vector form of Coulumb’s Law

Coulumb’s gives us force which acts between the charges and force is a vector so it is better to write Coulomb’s law in the vector notation. Let  and  are two point charge at the distance of r as shown in figure.

If is unit vector pointing from q1 to q2, then as per diagram  and  will be in the same direction, then

……………..(1)

And similarly If If is unit vector pointing from to, then as per diagram  and  will be in the same direction, then

……………..(2)

From the figure it can be seen that

So from equation (1) and (2)

…………………..(3)

Thus, Coulomb’s law agrees with the Newton’s third law.

 

Electrostatic Force between Two Point Charges In Terms Of Their Position Vectors

Let the position vectors of charges  and  be  and   respectively. We denote force on due to  by  and force on  due to by. The two point charges  and  have been numbered 1 and 2 for convenience and the vector leading from 1 to 2 is denoted by

……………….(1)

 

Figure: Position Vector Diagram of Charges

In the same way, the vector leading from 2 to 1 is denoted by r ₁₂:

………………………….(2)

The magnitude of the vectors    andis denoted by r₂₁ and r₁₂ respectively (r₁₂ = r₂₁). The direction of a vector is specified by a unit vector along the vector. To denote the direction from 1 to 2 (or from 2 to 1), we define the unit vectors:

and      ……………….(3)

Coulomb’s force on point charge  by point charge located at r₂ and r₁is then expressed as

………………………..(4)

 

From equation (3) and (4)

Or                      …………………………..(5)

From equation (5) and equation (1)

…………………….. (6)

Similarly

………………………(7)

By comparing equation (6) and (7)

……………………………………………….(8)

Thus, Coulomb’s law agrees with the Newton’s third law.