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 ρv at a velocity u = uy ay.
- Hence the current is given as:
Where uy is the velocity of the moving electron or ion and ρv is the free volume charge density.
- Hence the convection current density in general is given as:
J = ρv 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 (υd) 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 υd, 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 (μe).
υd = - μe E
where μe is defined as:
- Consider a conducting wire in which charges subjected to an electric field are moving with drift velocity υd.
- Say there are Ne free electrons per cubic meter of conductor, then the free volume charge density(ρv) within the wire is
ρv = - e Ne
- The charge ΔQ is given as:
ΔQ = ρv ΔV = - e Ne ΔS Δl = - e Ne ΔS υd 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 = ( Ne μe + Nh μh )e
- 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...
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