Courses

Courses for Kids

Free study material

Talk to our experts

1800-120-456-456

Dimensions of Charge in Physics: Definition, Formula & Uses

Q: 1. What is the dimensional formula of charge?

The dimensional formula of charge (Q) is [M0L0T1I1]. This means charge is fundamentally defined by time (T) and electric current (I), independent of mass (M) and length (L). It's crucial for understanding electrical phenomena and verifying the consistency of physics equations.

Q: 3. What are the SI units and CGS units of electric charge?

The SI unit of electric charge is the coulomb (C). In the CGS system, the unit of charge is the statcoulomb (statC) or electrostatic unit (esu). The coulomb is defined as the amount of charge that passes a point in a circuit when a current of one ampere flows for one second.

Q: 7. What is the difference between the dimensions of charge and charge density?

While charge (Q) has dimensions [M0L0T1I1], charge density depends on the type of density. Linear charge density (λ) has dimensions [M0L1T1I1], surface charge density (σ) has dimensions [M0L-1T1I1], and volume charge density (ρ) has dimensions [M0L-2T1I1]. The difference lies in how charge is distributed over space.

How to Derive the Dimensional Formula of Charge with Examples

The topic of Dimensions of Charge is important in physics and helps us understand various natural phenomena, instruments, and physical laws. For students preparing for JEE, NEET, and board exams, the dimensional formula of charge is a frequently asked and essential concept that connects electricity, electromagnetism, and modern physics.

Understanding Dimensions of Charge

Dimensions of Charge refer to the representation of electric charge in terms of fundamental physical quantities: mass (M), length (L), time (T), and electric current (I). This topic plays a vital role in Dimensional Analysis, verifying equations in Electricity, and solving problems in Current Electricity. Understanding the dimensional formula helps students detect mistakes and confirm the correctness of physics equations.

Formula or Working Principle of Dimensions of Charge

The dimensional formula of electric charge (Q) is derived using the relationship:
Q = I × T
where I is current, and T is time.

SI unit of charge: Coulomb (C)
Dimensions: [M⁰ L⁰ T¹ I¹]

Here’s a useful table to understand Dimensions of Charge better:

Dimensions of Charge Table

Concept	Description	Example
Charge (Q)	Product of current and time	A charge of 10 C flows in 2 seconds at 5A
Dimensional Formula	[M⁰ L⁰ T¹ I¹]	Derived using Q = I × T
SI Unit	Coulomb (C)	1 C = 1 A × 1 s

Worked Example / Practical Experiment

Let’s solve a dimensional analysis problem step by step:

1. Identify the known relationship: Q = I × T

2. Substitute dimensions: [Q] = [I][T]

3. [I] = [M⁰ L⁰ T⁰ I¹], [T] = [M⁰ L⁰ T¹ I⁰]

4. Multiply:
[M⁰ L⁰ T⁰ I¹] × [M⁰ L⁰ T¹ I⁰] = [M⁰ L⁰ T¹ I¹]

Conclusion: The dimensional formula of charge, [M⁰ L⁰ T¹ I¹], matches and confirms our calculation.

Practice Questions

Define Dimensions of Charge with an example.
What is the dimensional formula of charge in SI system?
How can the dimensions of charge help in verifying equations in electromagnetism?
What is the relation between charge, current, and time?

Common Mistakes to Avoid

Misinterpreting the unit (Coulomb) for the dimensional formula of Dimensions of Charge.
Confusing dimensions [M⁰ L⁰ T¹ I¹] with the SI unit (C) or mixing with related terms like current or charge density.
Applying charge dimensions wrongly while checking formulas involving electric field or force.

Real-World Applications

Dimensions of Charge are widely used in fields like electronics, electrical engineering, physics problem-solving, and checking the validity of equations in electromagnetism. By understanding dimensional analysis, students can identify mistakes in their solutions and better prepare for competitive exams. Vedantu helps you connect such core concepts with real-world physics applications, including calculations in circuits and verifying Law of Conservation of Charge or Coulomb’s Law.

In this article, we explored Dimensions of Charge — its meaning, formula, practical relevance, and usage in physics. Keep exploring such topics with Vedantu to improve your understanding.

Suggested Readings: Electric Charge, Current Electricity, Dimensional Analysis, Coulomb

FAQs on Dimensions of Charge in Physics: Definition, Formula & Uses

1. What is the dimensional formula of charge?

The dimensional formula of charge (Q) is [M⁰L⁰T¹I¹]. This means charge is fundamentally defined by time (T) and electric current (I), independent of mass (M) and length (L). It's crucial for understanding electrical phenomena and verifying the consistency of physics equations.

2. How do you derive the dimensions of charge?

The derivation stems from the definition of electric current. Current (I) is defined as the rate of flow of charge (Q) with respect to time (T): I = Q/T. Rearranging, we get Q = I × T. Substituting the dimensions of current ([I]) and time ([T]), we obtain the dimensional formula of charge as [M⁰L⁰T¹I¹].

3. What are the SI units and CGS units of electric charge?

The SI unit of electric charge is the coulomb (C). In the CGS system, the unit of charge is the statcoulomb (statC) or electrostatic unit (esu). The coulomb is defined as the amount of charge that passes a point in a circuit when a current of one ampere flows for one second.

4. Why do we use dimensions in physics?

Dimensional analysis is a powerful tool in physics. It helps to:

Verify the correctness of equations: Dimensions on both sides of an equation must match.
Derive relationships between physical quantities: Knowing the dimensions allows for the formulation of equations.
Check for errors: If dimensions don't match, there's an error in the equation or the derivation.

5. Is the dimensional formula of electron charge the same as for charge in general?

Yes, the dimensional formula for the charge of an electron is the same as the general dimensional formula for electric charge: [M⁰L⁰T¹I¹]. The electron charge is simply a specific, quantized value of charge (approximately 1.602 x 10^-19 Coulombs).

6. How is the dimension of charge related to current and time?

Charge (Q), current (I), and time (T) are related by the equation Q = I × T. This fundamental relationship directly shows that the dimension of charge is derived from the dimensions of current and time. One Coulomb is defined as the amount of charge transported by a current of one ampere in one second.

7. What is the difference between the dimensions of charge and charge density?

While charge (Q) has dimensions [M⁰L⁰T¹I¹], charge density depends on the type of density. Linear charge density (λ) has dimensions [M⁰L¹T¹I¹], surface charge density (σ) has dimensions [M⁰L^-1T¹I¹], and volume charge density (ρ) has dimensions [M⁰L^-2T¹I¹]. The difference lies in how charge is distributed over space.

8. What are the dimensions of charge in physics for JEE/NEET exams?

For JEE and NEET, the dimensional formula of charge remains consistently [M⁰L⁰T¹I¹]. Understanding this is key for solving problems involving dimensional analysis and verifying equations related to electromagnetism and current electricity.

9. How do I use dimensional analysis to check the validity of a physics equation involving charge?

Substitute the dimensions of each quantity in the equation. If the dimensions on both sides of the equation are identical, the equation is dimensionally consistent. However, dimensional consistency doesn't guarantee that the equation is entirely correct, only that it is dimensionally plausible. Inconsistency indicates an error.

10. What is the dimensional formula of charge in electromagnetism?

In electromagnetism, the dimensional formula for charge remains the same: [M⁰L⁰T¹I¹]. This is consistent across all electromagnetic phenomena, from Coulomb's law to Faraday's law of induction.

11. What are some common mistakes students make regarding the dimensions of charge?

Common mistakes include confusing the dimensions of charge with those of current or time, misunderstanding the relationship between charge and charge density, and neglecting the importance of dimensional analysis in verifying equations. Carefully distinguishing between charge and charge density is essential.