Field Theory - Conduction And Convection Current Density....

CONVECTION CURRENT DENSITY:


- Convection current occurs in insulators or dielectrics such as liquid, vacuum and rarified gas.

- Convection current results from motion of electrons or ions in an insulating medium.

- Since convection current doesn’t involve conductors, hence it does not satisfy ohm’s law.


- Consider a filament where there is a flow of charge ρ_v at a velocity u = u_y a_y.

- Hence the current is given as:

Where u_y is the velocity of the moving electron or ion and ρ_v is the free volume charge density.

- Hence the convection current density in general is given as:

J = ρ_v u

CONDUCTION CURRENT DENSITY:


- Conduction current occurs in conductors where there are a large number of free electrons.

- Conduction current occurs due to the drift motion of electrons (charge carriers).

- Conduction current obeys ohm’s law.


- When an external electric field is applied to a metallic conductor, conduction current occurs due to the drift of electrons.


- The charge inside the conductor experiences a force due to the electric field and hence should accelerate but due to continuous collision with atomic lattice, their velocity is reduced.


- The net effect is that the electrons moves or drifts with an average velocity called the drift velocity (υ_d) which is proportional to the applied electric field (E).


- Hence according to Newton’s law, if an electron with a mass m is moving in an electric field E with an average drift velocity υ_d, the the average change in momentum of the free electron must be equal to the applied force (F = - e E).

- The drift velocity per unit applied electric field is called the mobility of electrons (μ_e).

υ_d = - μ_e E

where μ_e is defined as:

- Consider a conducting wire in which charges subjected to an electric field are moving with drift velocity υ_d.


- Say there are N_e free electrons per cubic meter of conductor, then the free volume charge density(ρ_v) within the wire is

ρ_v = - e N_e

- The charge ΔQ is given as:

ΔQ = ρ_v ΔV = - e N_e ΔS Δl = - e N_e ΔS υ_d Δt

- The incremental current is thus given as:

- The conduction current density is thus defined as:

where σ is the conductivity of the material.

- The above equation is known as the Ohm’s law in point form and is valid at every point in space.


- In a semiconductor, current flow is due to the movement of both electrons and holes, hence conductivity is given as:

σ = ( N_e μ_e + N_h μ_h )e

ALSO READ: 

- Gauss's Law - Theory.

- Gauss's Law - Application To a Point charge.

- Gauss's Law - Application To An Infinite Line Charge.

- Gauss's Law - Application To An Infinite Sheet Charge.

- Gauss's Law - Application To a Uniformly Charged Sphere.

- Numericals / Solved Examples - Gauss's Law.

- Scalar Electric Potential / Electrostatic Potential (V).

- Relationship Between Electric Field Intensity (E) and Electrostatic Potential (V).

- Electric Potential Due To a Circular Disk.

- Electric Dipole.

- Numericals / Solved Examples - Electric Potential and Electric Dipole.

- Energy Density In Electrostatic Field / Work Done To Assemble Charges.

- Numericals / Solved Examples - Electrostatic Energy and Energy Density.

- Numericals / Solved Examples - Gauss's law...


- Short Notes/FAQ's

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