I read in my textbook that the average drift speed of electrons in a conductor is around 1mm/s, but when a switch is pressed the appliance gets turned on immediately……How does this happen? Can I get a detailed explanation if possible?
$\begingroup$
$\endgroup$
3
-
$\begingroup$ What about the electromagnetic field? $\endgroup$– HyperonCommented Dec 1, 2022 at 14:37
-
$\begingroup$ You don't need to wait for an electron to get from one end of the wire to the other for energy to be delivered. Electrons don't transport energy $\endgroup$– jensen paullCommented Dec 1, 2022 at 14:51
-
$\begingroup$ Drift speed is very limited, however interactions between electrons are spreading with light speed $c$. So at the moment you'll press on switch in your room, after a short period $\tau = \ell/c$, where $\ell$ is total length of wires from electricity source up to bulb,- electrons at bulb tungsten filament will start to feel pushed forward with drift speed. As long as it will happen, due to resistance, filament will experience Joule heating, and emit heat and electromagnetic light waves. $\endgroup$– Agnius VasiliauskasCommented Dec 1, 2022 at 15:44
Add a comment
|
2 Answers
$\begingroup$
$\endgroup$
The pipe analogy works well here.
Suppose you have a pipe full of water leading from a water tank to your faucet. You open the faucet a trickle.
Water immediately begins flowing all through the system. It immediately flows out of the faucet. The water that left is immediately replaced by water in the pipe behind it. Water in the tank immediately begins flowing into the pipe.
"Immediately" glosses over a point. It takes a very short time for the water in the tank to notice that water has been flowing out of the pipe. But how short?
Water in the pipe is under pressure. Water appears to be incompressible. But careful measurements show it can be compressed a tiny amount when pressure is applied.
When the faucet opens, the pressure at the faucet drops. Water from the pipe begins to flow. The water behind it is stretched a tiny amount. Water behind it pushes it forward. The water behind stretches a bit as its pressure drops. A pressure wave propagates up the pipe.
Sound is a pressure wave. The pressure wave travels at the speed of sound. So the delay for water to begin leaving the tank depends on the length of the pipe and the speed of sound.
Water in the pipe flows slowly because just a trickle is coming out. It is much slower than the speed of sound.
Current in a wire is much the same. Electrons begin flowing down the wire almost instantly. But they travel very slowly.
answered Dec 1, 2022 at 14:53
$\begingroup$
$\endgroup$
Some preliminary remarks.
You can use the circuit model as an equivalent of the field equations of the electromagnetic field as a good approximation, neglecting what happens outside the wires and the other elements (like resistors, capacitors,...) only when the time scale of the time-variant regime is significantly smaller than a time scale of the wave phenomena occurring outside the elements of the circuit, namely $\tau_c = \frac{d}{c}$: just as an example, long transmission lines have non-negligible interactions without the need of a conductor connecting two different lines; you get another example when you go to high-frequency regime, in oscillating currents in antennas that radiates electromagnetic field in the surrounding media.
Very weak signal may reach the light bulb as a consequence of the EM wave transmission in the media: anyway this is not perceivable by human eyes; light bulbs shine as a consequence of the motion of charges into conductor wires. There was a series of video of Veritasium on Youtube, and other guys that dissed him, before finally get a good experiment about the original setup of the video provided by AlphaPhoenix, https://www.youtube.com/watch?v=2Vrhk5OjBP8.
The word "immediately" should be translated as "in a interval of time much shorter than the scale of time of interest".
Answer.
The answer is in the continuity equation for electric charge,
- integral form: $\dot{Q}_V = -\Phi_{\partial V}(\mathbf{j}) = -\sum_k i_k$, i.e. the variation of the electric charge contained in a volume equals the net electric current entering the volume;
- differential form: $\partial_t \rho + \nabla \cdot \mathbf{j} = 0$,
In the limit of low-frequency regimes, with electrical components that can't store electric charges, the equations may be approximated setting time derivatives to zero as
- integral form: $\sum_k i_k = 0$, i.e. the net sum of the electric currents is zero across the boundary of a volume that can't store electric charges; in this regime, taking a section of electric wire, the electric current on one end equals the electric current on the other end;
- differential form $\nabla \cdot \mathbf{j} = 0$, meaning that the electric current density is a solenoidal field, like the velocity field in incompressible fluids, $\nabla \cdot \mathbf{u} = 0$. From this, you can think at the formal analogy from electric current at low frequencies and the motion of fluids in pipe when compressibility effects are neglected.
