Dimensional Formula of Electric Charge

Electric charges are the fundamental entity in electrostatics. Like mass, it is considered to be an elementary entity of an object. We know that the constituent particles of any object have charges (electrons and protons). Charges are conserved in nature. It simply means that the total number of positive and negative charges are constant. In the later sections, we will define electric charge, some of its properties, and deduce its dimensional formula.    

Formula of Electric Charge 

Coulomb is the SI unit of electric charge, which is the quantity of charge transferred in one second. Hence, electric charge is calculated as:

Q=I×t

Here,

Q is the electric charge

I is the electric current

t is the time

Dimensional Formula of Electric Charge

• 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, the dimensional formula of the following are:

• 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 electric charge can be written as:

[M0L0T1I1]

Definition of Electric Charge

Electric charge is a property by virtue of which a particle having charge experiences an attractive or repulsive force when it is placed in an electric or electromagnetic field.

Electric charge is a fundamental property, which means that we cannot break electric charge into any subcomponents. Mass is also a fundamental property, so we can assume it in the same way. Although electric charge has many properties, the most important properties are quantisation and conservation. 

Conservation means the total amount of charge in any  system is always constant. It is the sum of all the positive and negative charges.

Quantisation means that the charge that is present in any object will always be an integral multiple of the charge of an electron. It means the minimum charge that can exist is 1.602 x 10-19 Coulomb. 

Unit of  Electric Charge: The SI  unit of electric charge is Coulomb.

Electric charge is a scalar quantity because we only talk about the magnitude, not the direction. 

Primary Properties of Electric Charge

Electric charges are called point charges when the dimension of the electrically charged bodies is minimal. Let’s take note of the fundamental properties of electric charge. 

1. Additive property 

Electric charges are cumulative, and the type of electric charge they carry influences this property. It has a scalar value. It is possible to add the charges directly. Consider the following scenario: a system with only two charges, q1 and q2. The total charge for the system will be q1 + q2.

2. Conservative nature

A particle’s electric charge is conservative. It signifies that the charge can’t be created or destroyed. Conduction and induction are two mechanisms that can transfer charges from one system to another. 

3. Quantisation 

This is one of the fundamental properties of electric charge. The charge is technically a quantised quantity. The integral multiples of the basic unit of charge (i.e., 1.6 x 10-19 C) can be used to indicate a system’s net charge. If the body’s net charge is q, the equation can be stated as:

q = ne

n can be 1, -1, 2, -3, 4, -5, and so on. 

Conclusion

In these notes of the dimensional formula of electric charge, we studied how to deduce its dimensional formula and its properties. We now know that just like energy, charges cannot be created or destroyed. It is as fundamental as mass. But  we can separate them with the help of certain chemical reactions. Electrolysis is a good example to demonstrate this.