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Why is there an electric field only inside the resistor in the circuit (assuming that the wire has no resistance)?

If there is no electric field inside the wire, why does the electron move to the positive pole?

Peter Mortensen
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steve
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4 Answers4

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There is no electric field in a zero resistance wire, but with the exception of superconductors, all real wires have some resistance. In a superconductor electrons can freely move with no energy loss and therefore require no electric field.

The resistance of wires in a circuit is typically so low compared to resistors in the circuit that they are generally approximated as zero resistance conductors for the purpose of circuit analysis.

Hope this helps.

Bob D
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  • Thank you for the answer, but I still have a question. Even a superconductor, there must have a force to drive the electrons to flow in a uniform direction when the circuit is turned on, then after the electrons start the motion, the force disappear. – steve Jun 15 '21 at 23:02
  • Sure you need an energy source to start the process and thereafter it can be removed and the electrons will continue to move. A mechanical analogy is pushing a box on a friction less surface (analogous to a zero resistance wire). You give it a push (do work to accelerate it and give it a velocity) and the box theoretically moves on at constant velocity forever without any additional work. – Bob D Jun 15 '21 at 23:15
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The wire has the same potential everywhere if its resistance is zero. There is no force needed to keep the electrons flowing in it because of the very fact that its resistance zero. The positive pole has the same voltage as at the resistor. So inside the wire, there is a constant voltage and no electric field. But how can the electrons flow? What gives them their motion? They are kicked into the wire and battery pole by the inside potential and beacause the wire has no resitance they continue to have this motion. They are not slowed down by the resistance of the wire, as this is zero.

  • Thank you, but I don't really understand the reason why the electrons flow, where does that force come from? – steve Jun 15 '21 at 23:16
  • "So inside the wire, there is a constant voltage and no electric field", how can this be if voltage is a measure of electric field strength? Voltage is necessarily coupled with the electric field. The electric field is defined as $E = v/L$ where L is the length of the wire and v is the voltage. If there is voltage, then there is an electric field. – Tachyon Jun 15 '21 at 23:17
  • @Mr.Bohner The electrons get a first kick from the inside of the battery after which they keep this momentum, as there is no resistance in the wire. –  Jun 15 '21 at 23:20
  • @Tachyon The voltage can be constant over the wire. Only compared to Earth there is a difference in voltage. Maybe you mean something different with voltage. I see it as the field with constant potential energy. So the voltage in the wire is the same as the at the battery pole. –  Jun 15 '21 at 23:22
  • But a constant potential can still generate an electric field, or am I wrong? – Tachyon Jun 15 '21 at 23:24
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    I think the force is always directed to lower potentials and as the potential is constant there is no force. –  Jun 15 '21 at 23:25
  • I see what you mean. Yeah, that makes sense. I guess you are right then. Thanks. – Tachyon Jun 15 '21 at 23:26
  • You mean that after the first kick the electrons then follow the law of inertia keep the motion through the circuit, but the circuit is a loop, which means the electrons must have to turn round, and turn round also requires force, then what is that force? – steve Jun 15 '21 at 23:45
  • @Mr.Bohner Good one! That's a force that keeps their velocity constant, and it only is there at turns of the circuit. This force is delivered by the atoms (ions) in the wire. They "bend" (pull) the electrons in the right directions so they can't go outside the wire. Zero resistance is an ideal though. In reality, the electrons will always show dissipative behavior. –  Jun 15 '21 at 23:52
  • Assume there are two charged metal spheres, between them has a potential difference, now we connect them with a wire (zero resistance), is there still no electric field inside the wire before the charges on the spheres achieve balance? – steve Jun 15 '21 at 23:55
  • @Mr.Bohner Initially the field will be huge. It kicks all electrons at once to the other ball (with the less electrons). But when the charges flow (infinite current!) there is no field anymore. IF there is no resistance. –  Jun 15 '21 at 23:59
  • @Viesik One more question. In the moment of turning on the circuit, how does that "kick" affect the whole electrons inside the wire, even the shape of the circuit is irregular? – steve Jun 16 '21 at 00:14
  • Hi! I went to bed before I saw your post. It doesn't affect the electrons in the wire. Electrons are constantly kicked into the wire (by the battery power) and they keep their velocity because they don't meet resistance. The wire is a thing that directs the motion of the electrons without giving the electron resistance (only when the shape is not straight, adjusting forces are provided. –  Jun 16 '21 at 07:49
  • Thank you for taking so much time to answer my question. The electrons are kicked into the wire by the battery, then following the inertia to motion through the whole circuit, but I remember that my professor told us that when the circuit connect with the battery, the electrons in the wire start the motion almost the same time, so if the electrons are indeed kicked by battery to start their motion, then there must have a time delay in the different position of the wire. – steve Jun 16 '21 at 14:54
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Why there is an electric field only inside the resistor in the circuit (assuming that the wire has no resistance)

There is an electric field inside a resistor, or a capacitor for that matter is because there exists a potential difference across it. The potential difference exists because the battery deems so.

The wire doesn't have any potential difference across it -its an equipotential, an ideal conductor with zero resistance and hence can't hold an electric field inside.

If there is no electric field inside the wire, why does the electron move to the positive pole?

Oh no. The electron moves precisely because its experiencing an electric field - that created from the battery. Where does the electron go after leaving the negative terminal of a battery in a circuit? In the connected ideal wire? No. It goes straight to the resistor, then to the next component with the field.

But then why would one draw wires in circuit diagrams at all? That's because in real world circuits charge carriers do travel through wires to other components - they can' t jump through the intervening air gap$^1$ and need a conductive path. We carry forth this intuition in the form of an idealization while drawing circuit diagrams, drawing finite length ideal wires between circuit elements and showing currents even though, for this idealized diagram, the wires don't develop a field inside and play no role beyond that of showing connections.

$^1$ at lower than breakdown voltages

lineage
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  • "Where does the electron go after leaving the negative terminal of a battery in a circuit? In the connected ideal wire? No. It goes straight to the resistor, then to the next component with the field."

    If the current doesn't go via the superconducting wires to reach the resistors with the field, then how does it get there in the first place?

     – Tachyon Jun 15 '21 at 23:31
  • @Tachyon current transport in superconductors is different than the ideal $0$ LCR wires one draws in circuit diagrams. My point is that the wires drawn are symbolic - even without them with components connected end to end, the circuit would be the same. Whether one can actually do this or not is a real-life question where we use wires anyways. To reiterate, in ideal circuit diagrams, charges move only in regions of field. – lineage Jun 15 '21 at 23:40
  • So then, what is the difference between current flow in a superconductor and a 0 resistance wire? – Tachyon Jun 15 '21 at 23:43
  • @tachyon The fact that superconductors can 'digest' finite currents while our poor ideal wires can't ;) – lineage Jun 15 '21 at 23:44
  • So 0 resistance wires have infinite current while superconductors have finite current? I thought that superconducting wires were 0 resistance wires too. – Tachyon Jun 15 '21 at 23:47
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    @Tachyon and they are a quantum phenomenon. I am not sure if a classical idealization which is just a simplification tool, can even be extended to the much deeper phenomenon of resistance less flow, electrical or otherwise=e, merely because they share a characteristic. – lineage Jun 15 '21 at 23:49
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    @Tachyon they are both $0$ res. But there are no ideal wires in the world - things we deem wires have low but finite resistances, ideal wires can't and don't carry current, and superconductors are much richer and $\ne$ "a real-world ideal wire". – lineage Jun 15 '21 at 23:51
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    @Tachyon see https://physics.stackexchange.com/a/179386/226560 – lineage Jun 15 '21 at 23:52
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It doesn't take force to keep up motion. It takes force to generate motion. This is Newton's 2nd law.

Only if there are frictions, resistances and the like along the path will you have to exert a forwards force to maintain the motion. In an ideal wire, there are no sich resistances or frictions. So in an ideal wire, no electric force is needed. Charges will continue moving with constant speed effortlessly.

No wire is ideal, though. So no wire contains zero electric field. But it can be very small. The closest to zero is within superconductors.

Steeven
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