Dimensional Formula Of Charge

In the context of other matter containing charge, the charge is the fundamental feature of matter that exhibits electrostatic attraction or repulsion. Many subatomic particles have electric charge as a distinctive attribute. While placing a matter in an electromagnetic field, it tends to acquire an electric charge, which results in it experiencing a force. A charge can exist in positive or negative electric states (carried by protons and electrons). Charges with similar natures repel each other, while dissimilar charges attract each other. The object with no specific charge(+ve or -ve) is neutral.

Charge

The 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.

The electric charge is a scalar quantity. It has both magnitude and direction but is an exception to the general vector quantities. If it has been a vector quantity, the two charges meeting at one point will 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, and other units include Faraday, Ampere-Hour, etc.

Charge formula

Coulomb is the SI unit of electric charge that 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

What is the Dimensional Formula?

The equation or the formula, which is the set of specific fundamental units of any particular physical quantity provided with the degree of powers or number to express one unit of the amount, is termed a dimensional formula. It is generally expressed in the form of [MaLbTc].

Dimensional Formula of charge

The following dimensional formula of charge can be written as:

[M0L0T1I1]

Where,

M = Mass

I = Current

L = Length

T = Time

Derivation for the dimensional formula of 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 charge can be written as:

[M0L0T1I1]

Primary Properties of Electric Charge

The 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. 

Additive property of electric charge: 

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.

Conservative nature of electric charge:

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

Quantisation of charge: 

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

The dimension is the fundamental unit of any physical quantity, which helps us to acknowledge the facts ( the aspects of quantity expressed in mass, length, time, and various other perspectives) about the physical quantity. The dimensional analysis helps to find the relationship between two quantities and provides grounds for comparison and the conversion from one form to another. The dimensional formula of charge defines the fundamental units of an electric charge induced in an electromagnetic field that experiences the amount of force ( attraction or repulsion force) according to its nature.