# Coulomb’s law – Equation, Limitations,Vector Form

## Coulomb’s law

Coulomb’s Law gives an idea of the force between charges at two points. By the word point charge, we mean the size of linear charged bodies in physics is very small compared to the distance between them. Therefore, as it becomes easy for us to quantify the force of attraction / repulsion between them, we find them as point charges.

Charles-Augustin de Coulomb, a French physicist in 1784, measured the force between charges of two points and the concept that force being inversely proportional to the distance between charges.. He also found that this force is directly proportional (only magnitudes) to the sum of charges.

With the following clarification, we will prove it. Let’s assume there are two q1 and q2 charges The distance between the charges is’ r’ and the pressure between the charges is’ F.’ Then,

F ∝ q1q2

Or, F ∝ 1/r2

F = k q1q2/ r2

Where k is a proportionality constant equivalent to 1/4 π ε0. Here, ε0 is the epsilon naught and it indicates a vacuum permittivity. The value of k is 9/109 Nm2/C2 when we take a value of ε0 is 8.854 × 10-12 C2 N-1 m-2.from the S.I unit of value.

Like charges repel each other and unlike charges attract each other , according to this theory. It implies charges of the same sign pushing each other with repulsive forces while charges of opposite signs dragging each other with desirable force.

**Vector
Form of Coulomb’s Law-**

There are two types of physical quantities, namely scalars (with the only magnitude) and vectors (those with magnitude and direction). Force is a vector quantity as it has magnitude as well as direction. It is possible to rewrite the Coulomb rule in the form of vectors. The vector “F” is referred to as F, the vector r is referred to as r and so on.

Let there be two q1 and q2 charges respectively with r1 and r2 place vectors. Now, as both charges are of the same type, between them there will be a repulsive force. Let the q1 charge force due to q2 be F12 and the q2 charge force due to q1 charge be F21. The vector from q1 to q2 is the vector r21.

r21 = r2 – r1

To indicate a vector’s direction from position vector r1 to r2 and from r2 to r1 as:

Now the vector-shaped strength of charge q2 due to q1 is:

The above formula is Coulomb’s Law’s vector form.

**Coulomb’s Law Equation/Formula-**

The law of Coulomb states that the electrical force between two charged objects is directly proportional to the product of the charge on the objects and inversely proportional to the square of the distance of separation between the two objects. Coulomb’s law can be described as an equation

Where Q1 is the amount of load on object 1 (in Coulombs), Q2 is the amount of load on object 2 (in Coulombs) and d is the distance between the two objects (in metres). The symbol k is a fixed proportionality known as the constant of the law of Coulomb. The value of this constant depends on the medium in which the objects being charged are submerged. The value in the case of air is about 9.0x 109 N • m2/C2. The value of k can be decreased by as much as a factor of 80 if the charged objects are present in water. It is important to note that the units on k are such that the units on charge (Coulombs) and the units on distance (meters) are cancelled when replaced in the formula, leaving a Newton as the force unit.

The formula of the Coulomb law provides a precise description of the force between two objects whenever the objects behave as point charges. A charged sphere of conducting communicates with other charged objects as if all its charges were in its center. While the charge is spread evenly across the surface of the sphere, it can be considered that the center of charge is the center of the sphere. The sphere acts as a point load with its centered excess power. Since Coulomb’s law applies to point charges, the distance d in the equation is the distance for both objects between the centers of charge (not the distance between their nearest surfaces).

The symbols Q1 and Q2 in the formula of the Coulomb law represent the sum of charge on the two entities that interact. These quantities are often expressed as “+” or-” “values, since an object can be charged positively or negatively. The charging sign is simply representative of whether the object has an excess of electrons (an object charged negatively) or a shortage of electrons (an object charged positively). It may be tempting in the measurements of force to use the “+” and-” “symbols. Although the practice is not recommended, it certainly does not cause any harm. Using the “+” and-” “signs of force measurement would result in a”-” force value being a symbol of an appealing force and a “+” force value being a repulsive force. Mathematically, if Q1 and Q2 are of the same charge, the force value would be positive. And if Q1 and Q2 are of opposite charge, the force value would be found to be negative. This is consistent with the idea that objects charged against each other have an attractive interaction and have a repulsive interaction like charged objects. Ultimately, if you’re thinking conceptually (and not merely mathematically), you’d be able to determine the nature of force— attractive or repulsive — without using the equation’s “+” and-” “signs.

**Limitations
of Coulomb’s Law-**

Under certain conditions, Coulomb’s law is generalized and can not be freely used as other general formulas. The law is limited to the following points:

- we can use the equation if the charges are static (in resting position).
- The formula is simple to use when dealing with charges of normal and smooth shape and it becomes too difficult to deal with charges of irregular shape.
- The formula is only valid when the solvent molecules between the particles are considerably larger than both charges.

Also Read- What Is Electric Charge ?

Also Read – What is electricity ?

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