E field in a wire

[Jonathan Apps]

1. What is the electric field along a path through the air that starts at the + end of a battery, ends at the - end, and goes a large distance from the battery? In particular, what is the E field at those large distances?

2. Replace the path in 1. by the same path but along a wire between the + and - ends. What is the E field at large distances now?

3. And the point of this post is...... what causes the difference?

 

[anuttarasammyak]

Say you extend parallel wires from the ends of battery, plus minus charges distribute on their surface and change E, V around from what they used to be. Zero E inside the wire metal material. Then say you short circuit at the ends of the wires with a resister, by Ohm’s law points on it undertakes voltage in accordance with V of space around. If loop wire has homogeneous resistance, another pattern of wire surface charge distribution and E, V in space take place.

 

[SredniVashtar]

1. It is more or less an electric dipole field that decreases with distance

2. It is the value of electric field allowed by the constitutive relation in the material of the wire, that is Ohm's law in its local form. It could be very high if the conductivity of the wire is low (compatible with what the battery can supply due to its internal resistance)

3. Surface charge (and interface charge, if you change the material the wire is made of). It shapes the field inside the wires in such a way that it will follow the geometry and the constitutive relation.

See this https://electronics.stackexchange.c...ectric-field-in-a-wire-constant/532550#532550

 

[Baluncore]

3. And the point of this post is...... what causes the difference?

1. In the first case, no current flows through air, so the E-field will be a dipole field, centred halfway along the axis between the battery terminals.
2. In the second case, the battery is short-circuited by the wire, so there is almost no external E-field, rapidly falling to zero as the battery becomes discharged.
3. What causes the difference? Current flow.