Dimensional Formula of Coulomb

Coulomb’s Law is the mathematical expression of force exerted by charged objects on one another. (Analogous to Newton’s Law of Gravity.)

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

Electric charges

Electric charge is defined as the property of the matter that is due to its subatomic particles. It causes the material to experience a force when placed in a magnetic and electric field.

Electric charge is a scalar quantity. It has both magnitude and direction but is an exception to the general vector quantities. If it had been a vector quantity, the two charges meeting at one point would result in the vector sum of the total charges. But it is not the same as the sum of the combined charges due to two different charges connecting at one point to the algebraic sum of both. Hence, despite having magnitude and direction, electric charge is quantised as a scalar quantity only.

Its symbol is Q. 

The SI unit of electric charge is Coulomb. So the dimension formula of Coulomb will be the same as the electric charge.

Dimensional formula 

In terms of dimensions, a dimensional formula is an equation that expresses the relationship between fundamental and derived units (equation). The letters L, M and T are used to represent the three basic dimensions of length, mass, and time in mechanics.

All physical quantities can be stated in terms of the fundamental (base) units of length, mass, and time, multiplied by some factor (exponent). The dimension of the amount in that base is the exponent of a base quantity that enters into the expression. 

The units of fundamental quantities are expressed as follows to determine the dimensions of physical quantities:

• L = length 
• M = mass 
• T = time

Example: An area is equal to the sum of two lengths. As a result, [A] = [L2]. That is, an area has two dimensions of length and zero dimensions of mass and time. In the same way, the volume is the sum of three lengths. As a result, [V] = [L3]. That is, volume has three dimensions: length, mass, and time.

Dimensional Formula of charge

The dimensional formula of charge can be written as:

[M0L0T1I1]

So, the dimensional formula of Coulomb will also be [M0L0T1I1]

Where,

M = Mass

I = Current

L = Length

T = Time

Derivation for the dimensional formula of Coulomb

Current = Electric Charge / Time i.e I = Q / T …(i)

From equation (i) we can say 

Electric Charge = (Current).(Time) i.e Q = (I).(T)

Where, 

• Q is measured in Coulombs
• I is measured in Ampere
• T is measured in seconds

Therefore,

Current = [I1] …(ii)

Time = [T1] …(iii)

Substituting values from the equations (i), (ii), and (iii) 

Electric Charge = (Current).(Time) i.e Q = (I).(T)

Q = [I¹] × [T¹] = [T¹I¹]

Therefore, the resultant dimensional formula of Coulomb can be written as:

[M0L0T1I1]

Applications of Coulomb’s Law

The vector notation of Coulomb’s Law may be used to calculate force or 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 an object’s vector fields.

Conclusion

Coulomb’s Law defines the strength of the force between two charges that may be attracting or repelling each other. Hence, According to Coulomb’s law,  the electrostatic force between two different objects is dependent on the charge of the bodies. There are also few charged bodies in any substance known as neutrons. These bodies are neutral and help in generating electrostatic force. 

This can be represented by the following expression:

F= kq1q2/ r2 

Here,

F is the electrostatic force

K is Coulomb’s constant and is equal to 8.988*109 Nm2/C2

q1 and q2 are point electric charges

r is the distance between the two point charges.