How can electrons flow at a speed close to the speed of light if the drift speed is very less in conductors?
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Source : NCERT Science Textbook | Class 10 | Chapter : Electricity | Page : 201
Expecting professional answers only. Points : 25
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See the diagram of a simple DC circuit with a metallic conducting wire of length L connected to a battery of voltage V. Even if the calculations are not understood read the explanation.
We can estimate the high speed of electrons e⁻ (during short atomic distances) inside the wire this way:
Entire length L of the wire is filled with electrons in atoms. As soon as the switch is turned on on the battery, an Electric field E exists between the +ve terminal and -ve terminal. It is uniform along the distance L. That exerts a Coulomb's force F equally on each electron on the path.
Let V = 1.0 V. L = 1.6 m
Force F = q E = q V/d = 1.6 * 10⁻¹⁹ Coul * 1.0 V / 1.6 m
= 1.0 * 10⁻¹⁹ Newtons
Mass m = 9.1 * 10⁻³¹ kg
Acceleration of electron a = F/ m ≈ 1,100 * 10⁸ m/s²
Thus each electron gets pulled with an acceleration a that if it travels for 1 millisecond without any collision, it will attain a speed of 1.1 * 10⁸ m/s. This is very close to speed of light.
However, electrons jump from one atom into the neighboring atom. Many electrons try to jump into next atom along the path. So they collide with each other. So electrons cannot travel more than a some nanometers without a collision. After collision some electrons lose their speed. Again they accelerate at the above high rate. Each jump takes a little time too.
Thus the average speed of electrons reduces to 1 mm/sec. This is called the drift speed.
What happens is that all electrons along the path start simultaneously to drift exactly at the same time (practically). So an electron from the -ve terminal moves 1 mm in one sec. By this time an electron which is 1 mm behind the +ve terminal reaches that terminal. Thus current is established.
This is the reason why an electric bulb lights up immediately after switching on, even though electrons physically travel only at 1 mm/sec along the wire.
We can estimate the high speed of electrons e⁻ (during short atomic distances) inside the wire this way:
Entire length L of the wire is filled with electrons in atoms. As soon as the switch is turned on on the battery, an Electric field E exists between the +ve terminal and -ve terminal. It is uniform along the distance L. That exerts a Coulomb's force F equally on each electron on the path.
Let V = 1.0 V. L = 1.6 m
Force F = q E = q V/d = 1.6 * 10⁻¹⁹ Coul * 1.0 V / 1.6 m
= 1.0 * 10⁻¹⁹ Newtons
Mass m = 9.1 * 10⁻³¹ kg
Acceleration of electron a = F/ m ≈ 1,100 * 10⁸ m/s²
Thus each electron gets pulled with an acceleration a that if it travels for 1 millisecond without any collision, it will attain a speed of 1.1 * 10⁸ m/s. This is very close to speed of light.
However, electrons jump from one atom into the neighboring atom. Many electrons try to jump into next atom along the path. So they collide with each other. So electrons cannot travel more than a some nanometers without a collision. After collision some electrons lose their speed. Again they accelerate at the above high rate. Each jump takes a little time too.
Thus the average speed of electrons reduces to 1 mm/sec. This is called the drift speed.
What happens is that all electrons along the path start simultaneously to drift exactly at the same time (practically). So an electron from the -ve terminal moves 1 mm in one sec. By this time an electron which is 1 mm behind the +ve terminal reaches that terminal. Thus current is established.
This is the reason why an electric bulb lights up immediately after switching on, even though electrons physically travel only at 1 mm/sec along the wire.
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kvnmurty:
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Thanks a lot Sir! ♥
amazing
awesome answer sir !
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amazing answer sir !
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What is being confused here is not the flow of "current" but rather the transmission of energy.
The individual electrons in a wire move very slowly, as they can be modeled as constantly colliding with atoms (yes, this is a naive classical model, no quantum) and bouncing around randomly in the manner of a gas (the term "electron gas" is real and not inappropriate at all). Electric current is the very slow flow of this electron gas through the wire when an electric field is present. The term "flow of current" actually is misleading - there is no such "substance" called "current", current is a flow. "Flow of charges" or more specifically (in this case - in others, it may differ!) "flow of electrons" makes more sense. (After all, we don't talk about "current" as a substance which is contained within a river and which is what does the "flowing", i.e. "flow of current inthe river", rather we talk of flowing "water in" the river, and "the current" means the flow of water.)
The individual electrons in a wire move very slowly, as they can be modeled as constantly colliding with atoms (yes, this is a naive classical model, no quantum) and bouncing around randomly in the manner of a gas (the term "electron gas" is real and not inappropriate at all). Electric current is the very slow flow of this electron gas through the wire when an electric field is present. The term "flow of current" actually is misleading - there is no such "substance" called "current", current is a flow. "Flow of charges" or more specifically (in this case - in others, it may differ!) "flow of electrons" makes more sense. (After all, we don't talk about "current" as a substance which is contained within a river and which is what does the "flowing", i.e. "flow of current inthe river", rather we talk of flowing "water in" the river, and "the current" means the flow of water.)
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