A Very Long Wire

Electricity and Magnetism Level 2

Patrick has a wire so long that it can go to the moon and come back. Patrick made a simple circuit using this wire, a battery, a switch and a light bulb.

How much time will it take for the bulb to start glowing after the switch is closed?

Details and assumptions

The distance between Earth and Moon is about $\SI{384400}{\kilo\meter}$ .
The resistance of the wire is negligible.

About 1 second About 1 minute About 1 hour About 1 day The bulb will start glowing immediately

1 solution

Pranshu Gaba
Sep 19, 2016

Electric current is basically the flow of electric field. Its speed is finite, so it takes nonzero time for the current to flow through the entire circuit; it is not possible for the bulb to start glowing immediately. The speed of electric field is equal to $c$ in vacuum. Its speed in a wire is $c / \sqrt{\mu \epsilon}$ which is slightly smaller than $c$ : it is in the range $0.5 c$ to $0.9c$ depending on the material of the wire.

The distance between the earth and the moon is about $\SI{3.84 e8}{\meter}$ . Speed of light in vacuum is about $3 \times 10^8 \text{ m/s}$ , so the distance between Earth and moon is $1.28$ light seconds. The length of the wire can go to the moon and come back, so it is twice this distance, and is equal to $2.56$ light seconds.

Therefore the time taken for the bulb to glow is in the range of $2.56 \times \frac{1}{0.5}$ to $2.56 \times \frac{1}{0.9}$ seconds. This is close to $3$ seconds.

I think the answer should be: the bulb lights up immediately.

My logic >> current means flow of electrons. and it is not necessary that the electron has to come from that battery and pass through the whole wire and then hit the bulb to light it. when we say electron is flowing through a wire, we mean that electrons change their positions simultaneously. (it's more of like people standing in a row and each person coming a step forward. it doesn't take a while to come a step forward.)

Ishaan Rakib - 4 years, 8 months ago

Flowing of electric current is flow of information, and information cannot flow faster than light. Even in your analogy, it is not possible for each person to step forward simultaneously. There's some reaction time between two consecutive people moving forward, and that results in a finite speed of information flow.

Pranshu Gaba - 4 years, 8 months ago

It takes about one second for the electrical potential appears at end of wires, after the wires are connected to the battery, but it takes no time to the bulb starting to grow after the switch is closed.

Miguel Rozsas - 4 years, 7 months ago

Immediately

Sagar Arora - 4 years, 8 months ago

Information cannot flow faster than light, it can only travel at finite speed. Therefore it takes some positive time for information (switch has been closed) to flow in the circuit, and the bulb cannot glow immediately.

Pranshu Gaba - 4 years, 8 months ago

when information travel with infinite speed then.does it lost its some of information. i confused about energy realation and equivalence.

A Former Brilliant Member - 4 years, 7 months ago

But the switch and battery are presumably in the same room as the bulb. We're not talking about individual electrons making a round trip at the speed of light. All you need is a voltage drop across the light bulb.

Lawrence Pauls - 4 years, 7 months ago

We need an experiment to convince me, I agree that information cannot travel faster than light. But does this just depend on the distance from the switch to the bulb or the round trip distance of the circuit? I think the long wire will just function like a ground in this case and you will get a voltage drop immediately after you close the switch.

Lawrence Pauls - 4 years, 7 months ago

The round trip distance of the circuit would be necessary, as it needs to make sure that the circuit is indeed complete. The information must flow through the loop at least once to ensure that there are no breaks or branches in the circuit.

If we considered only the distance between the switch and the lamp, then it could be possible that the bulb switches on even though there is an open switch in the circuit far away from the switch. However, this cannot be true since the bulb cannot glow in an open circuit.

Pranshu Gaba - 4 years, 7 months ago

The feald is between the two conductors. So it doesn't have to be set up there and back

Jo Atkin - 4 years, 7 months ago

Yes, the speed of electrons is about the same of speed of light. But, once the battery is connected to the wire, the electrical potential flows through the wire, electron flow from positive side of battery and lacunes shows up from the negative pole until they reach the both poles of switch. When you close the switch the electrons have just to cross the small section of metal inside the switch. As soon a electron moves, other electron takes its place. This process continues, free electrons that already are in metal, changing positions. They not come from the battery. They not have to travel all the way. So, the answer should be immediately!

Miguel Rozsas - 4 years, 7 months ago

It is simply not possible to get a result with the data provided. We would need to know the position of the bulb switch and battery, we would also need to know about the history of swich positions and a the L C R of the cable and what the dialectic is made of .

If the person settings the question ever reads this , please Google how a transmission line works.

Jo Atkin - 4 years, 7 months ago

@Pranshu Gaba: Yes, the speed of electrons is about the same of speed of light. But, once the battery is connected to the wire, the electrical potential flows through the wire, electron flow from positive side of battery and lacunes shows up from the negative pole until they reach the both poles of switch. When you close the switch the electrons have just to cross the small section of metal inside the switch. As soon a electron moves, other electron takes its place. This process continues, free electrons that already are in metal, changing positions. They not come from the battery. They not have to travel all the way. So, the answer should be immediately!

Miguel Rozsas - 4 years, 7 months ago

A Very Long Wire

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