What is the dimensional formula of mobility and how is it derived?
The Dimensions of Mobility are fundamental in understanding current electricity and semiconductor behavior for JEE Main Physics. Mobility tells us how quickly charge carriers like electrons move when exposed to an electric field. It builds a bridge between drift velocity and the electric field, guiding exam questions and formula checks. Different materials and temperatures cause mobility to change, making it crucial for calculations in current electricity and electronics.
By definition, mobility (μ) is the ratio of the drift velocity (vd) of a charge carrier to the applied electric field (E):
μ = vd / E. This key formula plays an important role in the dimensional analysis of physics and helps check equations in competitive exams.
The dimensions of mobility allow you to quickly verify formulas, eliminate wrong options, and solve advanced MCQs in JEE Main. Understanding how to derive and use them is essential for accuracy. SEMANTIC_VARIANTS like “SI unit of mobility,” “mobility of electrons in physics,” and “formula of mobility” will appear in related questions. Vedantu’s method aligns with the JEE Main approach, using clear logic and exam-oriented steps.
Dimensions of Mobility: Derivation and Formula
Mobility (μ) is derived using basic quantities. Recall:
- Drift velocity (vd): Average velocity of charge carriers.
- Electric field (E): Force per unit charge at a point.
- μ = vd / E is the standard relation.
- The SI unit of drift velocity is m s-1. For E, it’s V m-1.
- Convert V (volt) using its dimensional formula for accuracy.
For dimensional formula, write steps as follows:
- μ = vd / E
- [vd] = [L T-1]
- [E] is electric field, and it’s [M1 L1 T-3 A-1]
- So, μ = [L T-1] / [M L T-3 I-1]
- This simplifies to [M-1 L0 T2 I1]
Physical Meaning, SI Units, and Comparison
Physically, mobility explains how easily electrons or holes respond to an electric field. Materials with high mobility allow charge carriers to move rapidly, as required in fast-switching devices.
| Property | Mobility (μ) | Drift Velocity |
|---|---|---|
| Definition | Charge velocity per field | Average carrier velocity |
| SI Unit | m2 V-1 s-1 | m s-1 |
| Symbol | μ | vd |
| Dimension | [M-1 L0 T2 I1] | [L T-1] |
| Related Formula | vd = μE | – |
The SI unit of mobility is m2 V-1 s-1. Always confirm symbol usage in calculation-based questions. Mobility differs from conductivity and resistance as it measures only the velocity response, not current or opposition.
Dimensions of Mobility in Numerical Problems
Practice with dimensions of mobility helps you in:
- Checking correctness of formulas using dimensional analysis.
- Solving JEE Main MCQs that mix up units or compare mobility types.
- Avoiding traps between electron and hole mobility.
- Calculating current in conductors or semiconductors using μ and charge carrier data.
- Connecting formulae with Ohm’s law and practical circuits.
Worked Example:
A semiconductor has electron mobility μ = 0.15 m2 V-1 s-1. If E = 300 V m-1, calculate drift velocity.
vd = μ × E = 0.15 × 300 = 45 m s-1.
The direct use of μ ensures correct units and answer.
You may find similar practice in Vedantu’s current electricity practice paper or JEE mock tests. For advanced applications, semiconductors may have different mobilities for electrons and holes, covered in device-level problems.
Summary Table: Dimensions of Mobility
| Aspect | Value / Symbol |
|---|---|
| Definition | Drift velocity per electric field |
| Formula | μ = vd / E |
| Symbol | μ |
| SI Unit | m2 V-1 s-1 |
| Dimension | [M-1 L0 T2 I1] |
| Application | Semiconductor and conductor calculations |
Common mistakes in using the dimensions of mobility include switching up numerator and denominator, confusing SI and CGS units, and mixing up carrier types. Always check calculation steps against exam requirements. Never use conductivity or resistivity values in place of mobility in derivations.
- Do not swap the electric field and drift velocity in the formula μ = vd / E.
- Check for negative signs (electron mobility is sometimes defined as negative for conventional direction).
- Review correctness of units in numeric problems.
- Don’t confuse the dimensions of drift velocity with mobility.
- Apply dimensional analysis to verify derivations in mock tests.
In practice, applying the dimensions of mobility is a powerful exam tool. Review related concepts and always verify units. For extra problems, see drift velocity, current electricity, and dimensional analysis on Vedantu. These internal links cover solved examples, revision notes, and advanced MCQs.
Understanding dimensions of mobility makes you more confident when solving material science and circuit-based JEE questions. Always use the correct dimensional formula, and review linked topics to connect ideas. Vedantu’s clear explanations and formula guides help you avoid exam errors and tackle numericals with speed.
FAQs on Dimensions of Mobility: Meaning, Formula, Derivation & Exam Guide
1. What is the dimension formula of mobility?
Mobility has the dimension formula [M0 L2 T-1 A-1]. This reflects its relation to drift velocity, unit electric field, and current. Key points:
- Mobility (μ) expresses how quickly charge carriers move through a material under an electric field.
- Derived from μ = vd/E, where vd (drift velocity) and E (electric field) are involved.
- The units simplify to m2 V-1 s-1.
2. What are the 4 dimensions of physical activity?
The four dimensions of physical activity describe its different aspects:
- Frequency: How often physical activity is performed.
- Intensity: How hard a person works during activity.
- Time: Duration of the activity session.
- Type: The kind of activity (e.g., walking, running, sports).
3. What is the unit of mobility (μ)?
The SI unit of mobility is m2 V-1 s-1.
- This unit reflects how fast charge carriers like electrons or ions move in response to an electric field.
- Mobility connects drift velocity (m/s) and electric field (V/m).
4. What are the dimensions of drift velocity?
The dimension formula for drift velocity is [M0 L1 T-1] as it is a type of velocity.
- Drift velocity describes the average velocity of charge carriers (like electrons) under an electric field.
- It is measured in meters per second (m/s).
5. What is the formula for mobility?
The formula for mobility (μ) is given by:
- μ = vd / E
- Here, vd is drift velocity and E is electric field strength.
- Mobility quantifies how quickly charge carriers move when an electric field is applied.
6. What is mobility in physics?
Mobility in physics refers to the measure of how easily charge carriers (such as electrons or ions) move through a material when exposed to an electric field.
- It shows the relationship between drift velocity and electric field.
- Higher mobility means charge carriers move more efficiently, which is important in conductivity.
7. What are the dimensions of mobility of electrons in current electricity?
The dimension formula for mobility of electrons in current electricity is [M0 L2 T-1 A-1].
- This matches the dimensional formula for mobility in general, relevant for class 11 and 12 physics.
8. What is the dimensional formula for mobility of charge carriers?
The dimensional formula for mobility of charge carriers (such as electrons, holes, ions) is [M0 L2 T-1 A-1].
- This shows how mobility connects drift velocity and electric field for any carrier in a conductor or semiconductor.
9. What is the SI unit and dimensional formula of mobility in class 12 physics?
The SI unit of mobility is m2 V-1 s-1 and the dimensional formula is [M0 L2 T-1 A-1].
- These are important for solving current electricity and semiconductor device problems in class 12 physics.
10. What is the formula for mobility in terms of charge and relaxation time?
Mobility (μ) can also be expressed as: μ = eτ/m
- Here, e is the charge of the carrier, τ is the mean relaxation time, and m is the mass of the charge carrier.
- This form relates the microscopic motion of carriers to their mobility.
