Current Electricity | Premium Physics Notes

Current Electricity - Mobility of Charge Carriers

Complete formula sheet, derivations, concept explanations, diagrams and exam-focused practice for CBSE Class 12, NEET, JEE Main, JEE Advanced, Olympiad, AP Physics, IB Physics and A-Level Physics.

If you are facing difficulty understanding Mobility of Charge Carriers, Mobility of Electrons, Mobility of Holes, Drift Velocity, Current Density, Conductivity, Semiconductors or IIT-JEE level Current Electricity concepts, contact Kumar Sir for one-to-one Physics guidance.
Contact: +91-9958461445 | Website: KumarPhysicsClasses.com

1. Formula Sheet First

Mobility connects microscopic motion of charge carriers with the macroscopic current measured in a circuit.

μ = v_d/EMobility definition

v_d = μEDrift velocity in field

I = nAqv_dCurrent through area A

J = nqv_dCurrent density

J = nqμEUsing mobility

σ = nqμConductivity

ρ = 1/σResistivity

v_d = eEτ/mDrude model

μ = eτ/mMobility from relaxation time

ρ = m/(ne²τ)Metal resistivity

σ_e = n_eeμ_eElectron contribution

σ = e(n_eμ_e + n_hμ_h)Semiconductor conductivity

Symbols

μ: mobility

v_d: drift velocity

E: electric field

n: carrier number density

A: area of cross-section

q: carrier charge

e: elementary charge

J: current density

σ: conductivity

ρ: resistivity

τ: relaxation time

m: mass/effective mass

n_e: electron concentration

n_h: hole concentration

μ_e: electron mobility

μ_h: hole mobility

Unit of mobility: m² V⁻¹ s⁻¹. Dimensional formula: [M⁻¹ T² A].

2. What Is Mobility of Charge Carriers?

Simple Definition

Mobility tells how easily a charge carrier can move through a material when an electric field is applied.

Formal Definition

Mobility is the drift velocity acquired by a charge carrier per unit electric field: μ = v_d/E.

Physical Meaning

High mobility means carriers gain larger drift velocity for the same electric field because collisions are less restrictive.

Importance

Mobility controls current density, conductivity, semiconductor speed, device performance and temperature behaviour.

3. Derivation of Mobility

By definition, mobility is drift velocity per unit electric field: μ = v_d/E.

For an electron in electric field E, the electric force magnitude is F = eE. The electron charge is negative, so its acceleration is opposite to E, but magnitude uses e.

Using Newton's second law, a = F/m = eE/m, where m is the effective mass in the material.

Between two successive collisions, the average time available for acceleration is relaxation time τ.

Therefore drift velocity magnitude becomes v_d = aτ = eEτ/m.

Substitute this in mobility definition: μ = v_d/E = (eEτ/m)/E.

Cancel E to obtain μ = eτ/m. Mobility increases with relaxation time and decreases with effective mass.

Collisions with lattice ions, impurities and phonons disturb the accelerated motion. A larger relaxation time means fewer collisions and hence larger mobility.

4. Mobility of Electrons

Electron mobility is μ_e = v_d,e/E. Electrons are negatively charged, so their drift is opposite to the applied electric field. Conventional current is in the direction of positive charge flow, therefore it is opposite to electron drift.

5. Mobility of Holes

A hole is the absence of an electron in a nearly filled valence band. It behaves like a positive charge carrier. Hole mobility is μ_h = v_d,h/E. Holes drift in the direction of electric field and contribute to conventional current.

Electron: negative carrier, drift opposite to E, usually higher mobility.

Hole: effective positive carrier, drift along E, usually lower mobility due to band structure.

6. Electron Mobility vs Hole Mobility

Point	Electron	Hole
Charge carrier	Actual electron	Vacancy acting as positive carrier
Direction of motion	Opposite to electric field	Along electric field
Charge	-e	+e
Mobility	Usually greater	Usually smaller
Role in current	Dominant in metals and n-type semiconductors	Important in p-type semiconductors
Metals	Primary carriers	Not used in simple metal conduction
Intrinsic semiconductor	Contributes with holes	Contributes with electrons
Extrinsic semiconductor	Majority in n-type	Majority in p-type
NEET/JEE importance	Direction, formula, conductivity	Semiconductor conductivity and comparison

Electron mobility is usually greater because electrons often move in bands with smaller effective mass and less restrictive hopping compared with holes in the valence band.

7. Mobility in Metallic Conductors

Metals contain many free electrons moving among fixed lattice ions. In an electric field, electrons accelerate but repeatedly collide with ions, impurities and phonons. The average time between collisions is relaxation time τ.

Conductivity relation: J = ne v_d and v_d = μE, so J = neμE. Since J = σE, σ = neμ.

When temperature increases in metals, lattice vibrations increase, relaxation time decreases, mobility decreases, resistance increases and conductivity decreases.

8. Mobility in Semiconductors

In intrinsic semiconductors, electrons and holes are thermally generated in equal numbers. In n-type semiconductors, electrons are majority carriers. In p-type semiconductors, holes are majority carriers.

Electron current density contribution: J_e = n_eeμ_eE.

Hole current density contribution: J_h = n_heμ_hE.

Total current density: J = J_e + J_h.

Therefore J = e(n_eμ_e + n_hμ_h)E.

Comparing with J = σE gives σ = e(n_eμ_e + n_hμ_h).

9. Temperature Effect on Mobility

Material	Temperature Increase Causes	Final Effect
Metals	Lattice vibrations increase, relaxation time decreases, mobility decreases.	Resistance increases and conductivity decreases.
Semiconductors	Mobility may decrease due to scattering, but carrier concentration increases strongly.	Conductivity increases and resistance decreases in usual intrinsic behaviour.

10. Mobility, Conductivity and Resistivity

Start with J = nqv_d.

Use v_d = μE, so J = nqμE.

Compare with Ohm's microscopic form J = σE.

Therefore σ = nqμ and ρ = 1/(nqμ).

Example 1

If n = 8 × 10²⁸ m⁻³ and μ = 4 × 10⁻³ m²V⁻¹s⁻¹, then σ = neμ = 8×10²⁸ × 1.6×10⁻¹⁹ × 4×10⁻³ = 5.12×10⁷ S m⁻¹.

Example 2

If μ doubles while n remains constant, conductivity doubles and resistivity becomes half.

11. Mobility and Drift Velocity

The relation v_d = μE means drift velocity is directly proportional to electric field for ohmic conditions. If voltage increases for fixed length, E = V/L increases and drift velocity increases. If length increases for fixed voltage, E decreases and drift velocity decreases. Area does not directly change v_d for fixed E, but it changes current I = nAqv_d. Temperature changes μ, so it indirectly changes v_d.

12. Dimension and Unit of Mobility

μ = v_d/E.

Unit of v_d is m s⁻¹.

Unit of E is V m⁻¹.

So unit of μ = (m s⁻¹)/(V m⁻¹) = m² V⁻¹ s⁻¹.

Since V = kg m² s⁻³ A⁻¹, dimension of μ = m²/(V s) = M⁻¹ T² A.

18. Diagrams and Visuals

13-17. Exam Practice Bank With Accordion Solutions

Click any question to open the answer and explanation.

19. Common Student Mistakes

20. Exam Strategy

CBSE

Focus on definitions, derivations, units, dimensions and direct formula application.

NEET

Memorise formula links: μ, v_d, J, σ, ρ and temperature effects.

JEE Main

Practise numerical chains combining E = V/L, v_d = μE and I = nAqv_d.

JEE Advanced

Handle multi-carrier conduction, graphs, varying field and semiconductor traps.

Olympiad

Build microscopic intuition: scattering, relaxation time, effective mass and model assumptions.

AP Physics

Connect microscopic current with circuit quantities and proportional reasoning.

IB Physics

Emphasise explanation quality, units, graph interpretation and uncertainty in models.

A-Level Physics

Practise drift velocity derivations, charge carrier density and resistivity links.

Still confused in Mobility of Charge Carriers, Electron Mobility, Hole Mobility, Drift Velocity, Conductivity, Resistivity or Semiconductor Current?

Learn step-by-step with Kumar Sir through one-to-one Physics mentoring.

Phone: +91-9958461445
Website: KumarPhysicsClasses.com