Coulomb’s law

STATEMENT: Coulomb’s Law states the amount of the force exerted by each charge on the other charge (remember Newton’s 3rd law).

                                        F = K(|q1| | q2| /r2)

The symbol k in this context refers to electrical forces and has nothing to do with spring constants or Boltzmann’s constant!

   K            =      9 × 109 N-m2/C2

 q1  & q2   =     electric quantities of two electric charges 

   r              =     distance between the two electric charges

   ε0            =     dielectric constant of vacuum

   F             =     force exerted on the electric charge with electric quantity q2 by the

                        electric, charge with electric quantity q1

When the charges are opposite, the force vector is drawn toward the other charge,

and when the charges are the same, the force vector is drawn away from the other charge.

Coulomb’s law is an inverse square law, exactly as the force of gravity between two masses. This indicates that the inverse square of the distance between two charges causes it to drop. In other words, twice as widely apart charges feel a quarter of the force. However, while its charge decreases with distance, it never reaches zero, giving it an endless range.

According to Coulomb’s inverse square law, the force of attraction or repulsion between two magnetic poles is directly proportional to the product of their pole strengths and inversely proportional to the square of the distance between them. It indicates that if two charged bodies, one positively charged and the other negatively charged, are held at a specific distance from each other, they will attract each other.

To calculate the force on a particular charge owing to several other charges, you first use Coulomb’s law to calculate the force on the charge due to each of the other charges separately,then add the vector sum of the forces to obtain the final result.

Importance of Coulomb’s Law:

Static Electricity: Coulomb’s law is what causes you to get startled when you touch a

doorknob after walking across the carpet. Electrons transfer via friction as you rub your feet across the carpet, leaving you with a net charge. All of your extra charges repel one another. As your hand approaches for the doorknob, an extra charge leaps over the conductor, creating a shock.

The electromagnetic force outweighs gravity by a factor of ten: While the electric and

Gravitational forces have many similarities, and the electric force has a relative strength of 10 times that of the gravitational force. Most goods are electrically neutral, meaning they have the same amount of protons and electrons, and gravity only appears huge to us because the earth we live on is so large.

Inside Atoms: Coulomb’s law also applies to interactions between atomic nuclei inside atoms.The Coulomb force repels two positively charged nuclei unless they are close enough for the strong nuclear force to win out. This is why great energy is required for nuclei to fuse as the repelling forces must be overcome first. Electrostatic attraction is also why electrons are drawn to atomic nuclei in the first place and why most objects are electrically neutral. 

Polarisation:When a charged object is brought close to a neutral object, the electron clouds around the neutral object’s atoms redistribute. Polarisation is the term for this occurrence. The electron clouds are pushed to the far side of the atoms if the charged item is negatively charged, causing the positive and negative charges in the atoms to be somewhat closer.

Due to the proportional distances between charges, Coulomb’s law states that the attraction between the negatively charged object and the positive charges in the neutral object will be somewhat larger than the repulsive force between the negatively charged object and the neutral object. As a result, there will be attraction even though one thing is formally neutral. This is why a charged balloon will not detach from a neutral wall!

Coulomb’s Law in vector form:

Because force is a vector variable, Coulomb’s law is better stated in vector notation. The position vectors for charges q1 and q2 are r1 and r2, respectively. Force on q1 due to q2 is denoted by F12, whereas force on q2 due to q1 is denoted by F21. The two-point charges q1 and q2 have been given the numbers 1 and 2 for convenience, and the vector going from 1 to 2 has been given the number r21.

                                                  r21  = r2 – r1

Applications of Coulomb’s Law:

The vector notation of Coulomb’s Law may be utilised to calculate the force or the electric field in a simple example where there are two point charges, one of which is a source charge.

Advantages:

It aids in the measurement of the distance between two electrically charged objects. The mathematical expression of Coulomb’s law may also be used to determine the direction between two charged objects. The formula may also be used to compute the object’s vector fields.

Disadvantages:

• It only applies to point charges that are at rest
• It can only be used in dosage circumstances when the inverse square law is followed
• When the charges are in an arbitrary form, applying Coulomb’s law is challenging. As a result, when the charges are in an arbitrary form, we cannot calculate the value of distance ‘d’ between them.

Conclusion

In the expression of Coulomb’s law, changing the sign or amount of a charge changes the electric field. There is a magnitude and a direction to the electric field. The electric field’s magnitude is directly influenced by how the charge is dispersed in space. The direction of the electric field at a place is shown by a line tangent to a field line. The electric field’s value is measured in terms of force per unit charge, and the SI units are newtons per coulomb. Finally, the force F per unit of positive electric charge q, which is the equation, determines the strength of an electric field E at any place. E=F/q.