Difference between conduction & convection current density?

In summary: The plasma current is the sum of an ionic current (carried by ions of mass m+) and an electronic current (carried by electrons of mass m-). In the case of a convective current, the electronic part of the current is small because the electron mobility is small. The main current is therefore the ionic current. This is why the term convection current is used.I think the main point of confusion is the term "convection current". In most cases, "convection" refers to the transfer of heat or mass due to the bulk movement of a fluid. In the context of electricity, "convection current" can refer to the movement of particles in a fluid that carries an electrical charge, such as in a plasma
  • #1
sams
Gold Member
84
2
Hello Everyone,

Could anyone please explain the difference between the conduction current density (J=σE) and the convection current density (J=ρvd)? I really appreciate any examples or applications to further elaborate these two theories.

Note: vd is the particles' average drift velocity.

Thanks!
 
Physics news on Phys.org
  • #2
Conduction current is something you would witness in a conducting material, such as a metal. It refers to the movement of current in the presence of an electric field and can be described by Ohm's law.

Convection current is current flow in an insulating medium. This, however, does not follow Ohm's law.

We can define current as the electric charge passing through an area per unit volume. [itex] I = \frac{dQ}{dt}[/itex] per unit time. Current density is the amount of current flowing through a surface per unit time [itex] J = \frac{\Delta I}{\Delta S}[/itex] with [itex]I = \int J \cdot dS [/itex].

In a convection current, we have a current flowing through an insulating medium [itex]\Delta I = \frac{\Delta Q}{\Delta t} = \rho\Delta S\frac{\Delta y}{\Delta t} = \rho\Delta S u_y [/itex] where S is the surface the current is passing through, y is the length along the velocity vector, and [itex] u_y[/itex] is the velocity vector. So we can express the convection current as [itex]J_y = \frac{\Delta I}{\Delta S}=\rho\cdot u_y [/itex]. Conduction current density will describe the ability for an electric field E to propagate through a medium, controlled by the proportionality constant sigma, or conductivity. So, both describe a "current", but it might be easier to replace the word "current" with "flow; convection describes the flow through an insulating medium, and conductivity describes flow through a conducting medium.
 
Last edited:
  • Like
Likes sams
  • #3
In the case of a convecton current, do we mean the case of an "insulating medium" by "dielectric of a capacitor?"
Does it experience an electric field?
What do we mean by "it does not follow Ohm's law?"
 
  • #4
Ohm's law is [itex] V=IR[/itex]. Voltage is an electric potential difference between two points which is therefore related to electric field. So conduction current, which is a function of electric field ([itex]J=E\sigma[/itex]), follows this law. Convection current expresses a flow due to convection, for example, a current flow due to a temperature or density differential between points. So it is not related to electric field, and therefore does not follow Ohm's law. An insulating medium would be a medium which does not conduct current (at least for a convection definition). An example of a convection current would be air in a house. If the air is heated at the bottom of the house, and the air is cooler at the top, the warm air rises due to a temperature (or density) differential. So you could define a current of air as it rose, which would be a convection current.
 
  • #5
I think there is some confusion here. ##\mathbf{J}=\sigma\mathbf{E}## describes charge flow in an Ohmic conductor. ##\mathbf{J}=\rho \mathbf{v}_{d}## is more general and can describe charge flow in any macroscopic situation with a drift velocity, including within a conductor.
sams said:
I really appreciate any examples or applications to further elaborate these two theories.
Here is a simple example. Let's say you wanted to find the drift velocity ##v_{d}## of the charges in a conductor with conductivity ##\sigma## in a uniform electric field of magnitude ##E##. Then relating the two equations gives
$$\sigma E=\rho v_{d}$$
Since ##\rho## is the number of charge carriers in a given volume, it can be expressed as
$$\rho=\frac{\rho_{m}ne}{m}$$
where ##\rho_{m}## is the density of the material, ##m## is the molecular mass of the material, ##n## is the number of free charge carriers per atom, and ##e## is elementary charge. The drift velocity is then
$$v_{d}=\frac{\sigma mE}{\rho_{m}ne}$$
 
  • #6
sams said:
Hello Everyone,

Could anyone please explain the difference between the conduction current density (J=σE) and the convection current density (J=ρvd)? I really appreciate any examples or applications to further elaborate these two theories.

Note: vd is the particles' average drift velocity.

Thanks!

Regarding electric conduction and convection currents, I see it in the following way when considering moving media. The electric conduction current is defined by I = σE where σ is the electrical conductivity of the medium and E is the electrical field measured in a system which is moving with the medium. As the medium itself moves with a certain velocity v with respect to a stationary reference system the total electrical current with respect to the stationary reference system can be written as

J = I + ρv

where ρ is the charge density in the moving medium.
 
  • #7
Lord Jestocost said:
Regarding electric conduction and convection currents, I see it in the following way when considering moving media. The electric conduction current is defined by I = σE where σ is the electrical conductivity of the medium and E is the electrical field measured in a system which is moving with the medium. As the medium itself moves with a certain velocity v with respect to a stationary reference system the total electrical current with respect to the stationary reference system can be written as

J = I + ρv

where ρ is the charge density in the moving medium.
This is not a correct interpretation. ##v_{d}## is the drift velocity of the charge carriers which is measured with respect to a stationary conductor.
 
  • #8
NFuller said:
This is not a correct interpretation. ##v_{d}## is the drift velocity of the charge carriers which is measured with respect to a stationary conductor.

I think the OP made a mistake confusing something (or he/she should indicate what the terms in J = ρvd mean and where he found this equation). Convection currents are proportional to the charge density ρ. Even if ρ = 0, you can have conduction currents.

EDIT: As far as I remember, the term convection current is used when addressing the current density of plasmas.
 
Last edited by a moderator:

1. What is the difference between conduction and convection current density?

Conduction current density refers to the flow of electrical current through a material, while convection current density refers to the flow of a fluid or gas due to differences in temperature or density.

2. How do conduction and convection current density affect heat transfer?

Conduction current density is the dominant mechanism for heat transfer in solid materials, while convection current density is responsible for heat transfer in fluids or gases.

3. Can conduction and convection current density occur simultaneously?

Yes, conduction and convection current density can occur simultaneously in some materials, such as in fluids or gases with temperature gradients.

4. How is convection current density related to natural convection and forced convection?

Natural convection refers to the movement of a fluid due to density differences caused by temperature variations, while forced convection is the movement of a fluid caused by an external force. Convection current density is the measure of the flow of the fluid in both cases.

5. How can conduction and convection current density be calculated?

Conduction current density can be calculated using Ohm's law, which relates current density to electric field and conductivity. Convection current density can be calculated using the convective heat transfer coefficient and the temperature difference between the fluid and its surroundings.

Similar threads

  • Engineering and Comp Sci Homework Help
Replies
7
Views
586
  • Special and General Relativity
Replies
3
Views
2K
  • Atomic and Condensed Matter
Replies
1
Views
4K
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
2K
Replies
13
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
2K
Replies
2
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
1K
Replies
2
Views
2K
Back
Top