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Electric field inside the conductor is zero. That means there is no electric force on electrons inside. Then how do free electrons move from atom to atom in random direction? What is the reason of this random movement? Sorry if this question looks very basic.

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  • $\begingroup$ see hyperphysics.phy-astr.gsu.edu/hbase/electric/miccur.html $\endgroup$
    – anna v
    Mar 12, 2023 at 19:31
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    $\begingroup$ If electrons move, the field isn't zero. $\endgroup$ Mar 13, 2023 at 9:34
  • $\begingroup$ > "Electric field inside the conductor is zero." Only macroscopic electric field in perfect conductor, or in real conductor in electrostatics. Otherwise it need not vanish. Also microscopic electric field in real conductor does not vanish even in electrostatics, electrons experience electric field of other electrons and nuclei. $\endgroup$ Mar 13, 2023 at 16:03
  • $\begingroup$ Related: youtube.com/watch?v=oI_X2cMHNe0 - Veritasium - How Electricity Actually Works. He covers some good stuff about electric fields in and around conductors, and how quickly they propagate when you close a switch. $\endgroup$ Mar 14, 2023 at 3:13

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The electric field is only $0$ in the electrostatic case. That is, the field is $0$ when no electrons are moving.

Suppose it was not $0$. Electrons would feel a force and move in that direction. This reduces the electric field. They move until it is $0$.

To see why the movement reduces the field, consider this example. Suppose a wire has a + charge at one end and a - charge at the other. This sets up a field from + to -. Electrons have a - charge, and so feel a force in the opposite direction of the field. That is, they are attracted to the + charge, and repelled by the - charge. Electrons flow away from the - end and toward the + end until they have balanced the charges.

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  • $\begingroup$ This doesn't answer the question. The OP seems to understand that inside the conductor the field is 0 (but missed the "electrostatic" case, which you correctly pointed out). The OP didn't ask for why the field is 0, but why the electrons still move when the field is (apparently) 0. $\endgroup$ Mar 15, 2023 at 14:13
  • $\begingroup$ @LorenzoDonatisupportUkraine - It isn't a complete answer. It addresses what he asked in the title. Bob D (+1) addressed the rest. $\endgroup$
    – mmesser314
    Mar 15, 2023 at 15:12
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Then how do free electrons move from atom to atom in random direction?

The random movement of electrons in a conductor is thermal motion. It exists regardless of the presence of an electric field. The introduction of an electric field causes the randomly moving electrons to additionally collectively "drift" in the direction opposite to the direction of the field.

Hope this helps.

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One should be aware of the various statements made in the context of different models.

Ideal metal
Ideal metal is a concept often sued in electrostatics - metal is assumed to have an infinite amount of charge that can flow inside it. If there is an electric field present inside a conductor, the conductor, the charge would flow to screen this electric field, until the field is fully screened (i.e., becomes zero). Hence the electric field inside a conductor in equilibrium is always zero.

Macroscopic electrodynamics
Electrostatics is only a subset of the field called macroscopic electrodynamics, which considers electric and magnetic fields average over a physically small volume, that is the fields considered are averages over volumes containing macroscopic number of atoms/molecules ($N_A\approx 10^{24}$), but small compared to the distances relevant to the phenomena described, so that we can still describe them by continuous differential equations. Whenever we talk about local properties like conductivity, dielectric permittivity or magnetic permeability we speak of macroscopic electrodynamics and average fields. See Macroscopic Maxwell equations.

Microscopic fluctuations in statistical physics
Of course, the microscopic fields are never zero. Even if we assumed that the atoms and electrons do not move, the electric field would vary wildly over space, as we move from atom to atom. Including the atomic and electron thermal motion doesn't change much here. However, as we always do in statistical physics, we can talk about the mean/average field and about its fluctuations - just like we talk about constant pressure, which really results from single molecules tapping against a surface.

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An electric field of zero means that electrons are not accelerated. Since electrons are so light-weight and so absurdly numerous within any conductor, strong electric fields cannot exist for relevant times within a good conductor. The electrons will immediately move to compensate the electric field. That is why we can simplify thinking about conductors by saying that there is no electric field within. That has the nice consequence that we can simply model a conductor like a single entity with only a single potential value. But, it is only a simplification.

Reality, however, is more complex. It is true that, for electrons to be accelerated, there must be an electric field. And this happens in two very important use cases:

  • Very fast voltage changes need time to propagate through a wire. The speed of light is high, but finite. Consequently, you get potential waves propagating along the wire. And wherever the potential changes along the wire, there must be a transient electric field within the wire.

    The consequence is, that the 32 bits of an IPv4 address occupy less than ten meters of Gigabit Ethernet cable. If the cable is longer, the sending computer is done with sending the last bit before the receiver sees the first bit on the line. At this point in time, you have more than 32 regions of potentially different voltage levels on the same physical wire, with up to 31 areas of wire in between where there is an electric field within the wire. This entire wave moves swiftly along the wire, so that the receiver will see each of the 32 bits arriving one after the other over the course of 32 nanoseconds.

  • Non-superconducting wires act like resistors. I.e. whenever there is a current within the wire, there is also a potential difference between the ends of that same wire. And this translates to a low electric field along the length of the wire. It is this electric field that is constantly accelerating the electrons along the wire, replenishing their kinetic energy between their collisions with the atoms of the metal. The higher the resistance of the wire, the stronger the electric field for the same current.

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