Electric Field inside wires of Circuit?

[ee15]

Homework Statement

This is not a homework problem but I only have permission to post here because I am new.

My question is about the electric field in the wires of a simple circuit with a battery and a resistor. Electrons from from lower potential to higher potential terminal battery, meaning there must be an electric field in the wires. Can we determine the electric field knowing that the battery produces a voltage ΔV?

Homework Equations

\vec{E} = \nabla[ ΔV(x,y,z) ]

The Attempt at a Solution

I don't think the formula for \vec{E} is useful as we don't know the potential as a function of anything.

One thing that might make sense is that \vec{J} = \sigma\vec{E}, the current density is proportional to the electric field. This is not very intuitive to me, however, is the current density, and by extension electric field, simply a function of the dimensions of the wires?

 

[Simon Bridge]

That would be a "not really" with a "sort of" tacked on.
The current density inside a wire varies by radius... highest at the outside (electrons repel each other). BTW: that relationship is just ohm's law.

What do you need to know for and at what level?

 

[ee15]

I need to know because this is a source of confusion I have come across in my readings of electricity and magnetism. I seek an answer the maximum level possible / to the best of your understanding. Thanks.

 

[Simon Bridge]

Sorry - your stated needs are too general. I can only answer specific questions. I need to know your knowledge level in order to talk to you.

For the depth you are talking about, you are advised to do a college physics course to post-graduate level.

 

[ee15]

The reason I am asking is I because a fourth year (undergrad) circuits course I am taking requires knowledge of electric fields in a circuit. The online material regarding this subject is difficult to find (I have searched without much success), which is why I posted here in hope someone can help explain this phenomena. Please feel free to assume I have enough knowledge to understand your explanations.

 

[Simon Bridge]

OK - since you are a senior undergrad I don't have to do a blow by blow for you either ;)

You will want Maxwel's equations then: look to the relationship between electric and magnetic fields. I'd suggest, as an exercise, applying them to a solid wire with an applied PD along it's length... the online material is usually couched in terms of finding the magnetic field inside a wire.

It is common to approximate the current density inside a wire of circular crossection as a quadratic with radius. It is also a tricky calculation for non-trivial geometries. The distribution of charge affects the potential, which affects the distribution of charge ...

A course in circuits is usually more interested in design - the main concern is the effect stray fields have on adjacent tracks on a circuit board - something that is usually accounted for by rule-of-thumb, buffers, and tuneable components. eg. it is something you measure more than calculate.

The question is still pretty non-specific.

 

[aralbrec]

ee15, you're a fellow traveller :)

Have a read here to gain a conceptual understanding in DC circuits:
http://science.uniserve.edu.au/school/curric/stage6/phys/stw2002/sefton.pdf