ELECTRIC field due to a solenoid, or a current-carrying wire, or

[AxiomOfChoice]

We always talk about the magnetic field produced by solenoids, straight wires of current, and rings of current, etc., but why do we never talk about the ELECTRIC fields produced by these geometries? I mean, there are CHARGES, right? So there must be electric fields present, right? Or am I wrong?

I know a CHANGING magnetic field produces an electric field, but why don't STEADY currents produce electric fields?

 

[Dale]

This just follows directly from Maxwell's equations. With no changing B field the E field has no curl (Faraday's law), and with no net charge the E field has no divergence (Gauss' law). A field with no curl and no divergence is identically 0.

 

[jtbell]

Current-carrying wires contain equal amounts of positive and negative charge, and are electrically neutral.

 

[abhishekkgp]

. A field with no curl and no divergence is identically 0.

well, it may be constant in general. in case of wire with conductivity sigma, there is electric field inside the wire( given by ohm's law).. although if the current is steady and the conductivity uniform the divergence of the electric field becomes ZERO.
is the curl of electric field in this case also zero? i guess it should be because charge density in this case is constant with time everywhere.

 

[sardar]

You are correct, there are electric fields present in these geometries due to the presence of charges. However, the reason we often focus on the magnetic field is because it is typically much stronger and more easily measurable in these situations. The strength of the electric field is directly proportional to the charge, whereas the strength of the magnetic field is proportional to the current. In most cases, the current is much larger than the charge, making the magnetic field more significant.

Additionally, the electric field produced by a steady current is typically small and uniform, whereas the magnetic field can vary greatly in strength and direction. This makes the electric field less noticeable and less commonly discussed in these situations.

However, it is important to note that both the electric and magnetic fields are present and play important roles in understanding the behavior of these geometries. In fact, the interplay between the two fields is what allows for phenomena such as electromagnetic induction, where a changing magnetic field can create an electric current.

Overall, while the electric field may not be as prominent in these situations, it is still an important factor to consider and is always present in conjunction with the magnetic field.