Coulomb’s Law And Clarity On The Concept

Coulomb’s law, or Coulomb’s inverse-square law, is a physical experiment that determines the amount of force connecting two particles which are in fixed position but are electrically charged. Electrostatic force, also known as Coulomb force, is the electric force connecting charged bodies at rest. Coulomb’s law for electrostatic force quantifies the amount of force between two stationary, electrically charged particles and can be better understood with an experiment on Coulomb’s law.

Electrostatic force between two point charges

• According to this law, The electrostatic force between two point charges q1 and q2 

1. is directly proportional to the product of their magnitude of charges.

Feq1q2…………(1)

2. is inverse proportional to the square of distance between two point charges.

F1r2……………(2)

• By equation (1) and (2), we can write,

Fq1q2r2

F=140q1q2r2

• The force is along the line joining the point charges.

Where, 0=permittivity of free space=8.8510-12C2N-m2

140 =9109N-m2C2

• If both point charges are surrounded by a medium of dielectric constant or relative permeability denoted by K or r, then the electrostatics force becomes,

F=140rq1q2r2

     =14mq1q2r2, where m=0r is the permittivity of the medium.

• Electrostatic force is an inverse square force, therefore it is conservative in nature.

Coulomb’s law in Vector Form

• The vector form of coulomb’s law is given by,

Relative position of q2 with respect to q1 is r21. Therefore, Force on charge q2 by q1 is, Fq2/q1=140q1q2r212r21=140q1q2r2–r13(r2–r1)

• Put the values of charges with a sign while applying the vector form of coulomb’s law.

• Electrostatic force follow’s newton’s third law,

Fq2/q1=-Fq1/q2

Relative permittivity of Dielectric constant

• It is the ratio of permittivity of the medium to permittivity of free space.

K or r=m0, where m is the permittivity of the medium.

• For Air and Vacuum, r=1

For Metals, r

Superposition principle

• This principle is used to find the resultant force on a charge particle when there are several numbers of charge particles placed in its surrounding. 

• According to the superposition principle, the force between two charges is independent of presence or absence of the third charge.

• Therefore, the net force on a charged particle is the vector sum of electric forces by all the charges present in its surroundings. 

Fnet=F1+F2+F3+…………

 Equilibrium of charge

1. If any charge particle is at equilibrium then net force on that charge particle is zero.

⇒ Fnet=0

2. To check the type of equilibrium, displace the charge particle by small displacement x from the equilibrium position and calculate the net force on the charge particle at displaced position:

• If the net force is directed towards the initial position, then point charge is said to be in stable equilibrium

• If Fnet is not directed towards the initial position, then point charge is said to be in unstable equilibrium

• If Fnet=0, then point charge is said to be in neutral equilibrium

Solved example

Example 1: Three q-valued point charges are positioned on three vertices of a perfect square with side a. What is the magnitude of the force on a -q coulomb point charge put in the square’s centre?

Solution:

The given situation can be drawn as shown below,

Let us assume a square(ABCD) of side a and positive charges are placed at the vertices A, B and C and negative charge is placed at centre O.

The distance between centre and vertex of the square is,

r=a2

The electric forces on -q are shown in figure.

 The electric force by A and C are equal and opposite as they are placed at the same distance. Therefore,

FO/A+FO/C=0

Now, The net force on the -q charge is given by superposition theorem,

(Fnet)O=FO/A+FO/B+FO/C

(Fnet)O=0+FO/B

Therefore, the net force at O is,

|FO|=|FO/B|=140q2r2

|FO|=140q2(a/2)2=1402q2a2

Example 2: Two point charge of charges Q and 4Q are placed at a separation of d. Where should a third charge q should be placed so that the system is in equilibrium. Also find the value of q.

Solution:

The situation given is shown below,

System is in equilibrium therefore we can say that each and every point charge will have zero net force.

To the left of A and right of B the direction of electric force is in same direction so the net force can not be zero on q. Therefore, the third charge q should be placed in between the given charges as shown,

At equilibrium,

(Fnet)q=0

FA–FB=0

FA=FB

140Qq(d-r)2=1404Qqr2

(d-rr)2=14

d-rr=12

r=2d3

Therefore the third charge q should be placed at a distance of 2d3 from 4Q.

The system is given in equilibrium. So net force on A should also be zero.

The net force on A is given by,

(Fnet)A=0

FB+FC=0

140Qq(d-r)2+140(4Q)(Q)(r)2=0

q=-Q(d-rr)2

q=-Q(d/32d/3)2……….(r=2d3)

q=-Q4

 Conclusion

Coulomb’s Law is a formula for calculating the electric force that exists between two electrical charges. It allows you to calculate the directionality and strength of the corresponding electric force.According to Coulomb’s law, the main attribute of the electric force for particles at rest is that like charges repel against each other while unlike charges attract towards each other