Dimensions of Electric Charge

What is the Dimensional Formula of Charge?

Dimensional Formula of Charge is [M⁰L⁰A¹T¹]

Charge is a fundamental property of the matter that tells us about the electromagnetic property of the matter. Charge can be easily categorized into two categories that are, Positive change and Negative Charge. Now let’s learn about Electric charge, its formula, and the Dimensional formula of charge in detail.

What is Electric Charge?

Electric charge is a fundamental property of subatomic particles that gives rise to the phenomenon of experiencing force in the presence of electric and magnetic fields. In the presence of these fields, there are some observable effects experienced by charged particles.

There are two types of electric charge:

• Positive Charge: Protons (p)
• Negative Charge: Electrons (e)

Types of charges

Electric Charge Formula

Since we define electric charge as a product of current flowing in a certain time.

Mathematically charge is represented as

Q = I.T

where,

• Q represents the Electric Charge
• I represents the Current Flowing
• T represents the Time

Derivation of Dimensional Formula of Charge

We derive a dimensional formula of charge. Since we can say the charge collected in a conductor having current in time t is represented as

Charge(q) = Current× Time

Dimensional formula of q = dimensional formula of (Current × Time)…(1)

Now we calculate the dimensional formula of each quantity individually

Dimensional formula of I = [M⁰L⁰A¹]

Dimensional formula of T = [M⁰L⁰T¹]

Putting all the above three-dimensional formulas in Equation (1) we get

Dimensional Formula of Charge = [M⁰L⁰A¹] × [M⁰L⁰T¹]

Dimensional Formula of Charge = [M⁰L⁰A¹T¹]

Hence, the dimensional formula of Charge is [AT]

Advantages of Dimensional Formula

There are various advantages of representing a physical quantity through its dimensional formula:

• It can be used to check the consistency of a dimensional equation.
• It can be used to derive the relation between physical quantities in physical phenomena. Like in equation v = u + at, we can relate acceleration and time.
• It can be used to change units from one system to another conveniently.
• It can be used to find the dimension of constants in a given relation.

Limitations of Dimensional Formula

The major limitation of the dimensional formula is that it can’t be used to verify if the formula for a given quantity is correct or incorrect.

For example, v = u m/sec and v = at m/sec,

Both are dimensionally correct but the formula is not correct. The correct formula is v = u+at m/sec (first law of motion). So we can’t derive the correct formula from dimensions with surety.

Learn More Dimensional Formulas

• Dimensional Formula of Coefficient of Viscosity
• Dimensional Formula of Potential Energy
• Dimensional Formula of Magnetic Flux

Dimensional Formula of Charge- FAQs

1. What is Dimensional Formula?

Dimensional Formula is a representation of any quantity in terms of 7 fundamental quantities.

2. What is Charge?

Electric charge can be defined as a fundamental property of subatomic particles.

3. What is the SI Unit of Charge?

We can derive the SI units of electric charge from its dimensional formula. The dimensional formula of charge is [AT] so its SI unit is Ampere-Second or Coulomb .

4. What is Coulomb?

Coulomb is not a separate physical quantity, instead, it’s the SI unit of charge. Hence, it will have the same dimensional formula as the charge, [ M⁰L⁰T¹A¹ ].

5. What is Dimensional Formula of Electric Charge?

Electric charge and charge are the same, so they have the same dimensional formula. The dimensional formula is [ M⁰L⁰T¹A¹].