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Suppose I have a long metal copper wire (for example $100\ \mathrm{m}$ or $1\ \mathrm{km}$) and put it vertically on the earth's surface, then I put direct current (DC) of 1 ampere into it. I make it in a way that the negative end is on top, and electrons go down from the top of that wire to the bottom inside the wire.

I'm wondering, if I put 2 ammeters to measure the current inside this wire, one on the very top and one on the very bottom, will the gravitational field cause them to show different readings?

I would expect that electrons will be accelerated by the earth's gravitational fields and they will be moving faster at the bottom of the wire. Based on this article, electric current does depends on the electrons' velocity. If the electric current will be different, then what approach could I use to calculate the difference? Is there a well-known effect on electric current in a gravitational field or accelerated non-inertial frame? If so, I would appreciate the name of that effect or a link where I can read more about it.

The question is theoretical, so please do not get hung up on details like how I cannot make a $1\ \mathrm{km}$ vertical wire because of the strength of the materials, etc. Also, let's assume that the ammeters do not influence the wire and the electric current inside it, maybe contactless ammeters based on the magnetic field or something similar.

David Z
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Zlelik
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2 Answers2

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In the absence of other forces, then gravity can indeed affect the motion of charged particles. But these forces are very weak in comparison to the forces from other charged particles nearby.

If the electrons were moving faster as they neared the earth, this would cause them to bunch up and repel each other more strongly. Also, a larger gap would open above them and the repulsion from other electrons above would be smaller. Together, these forces would overwhelm the gravitational force and tend to return the circuit to a steady flow throughout.

For any circuit, this must be true regardless of what might be affecting the charge flow. If we consider the total charge in the circuit to be constant, then any difference in current between two points could only be temporary, or the higher current section would run out of charge.

Is there a well-known effect on electric current in a gravitational field or accelerated non-inertial frame?

In another answer there is a reference to the Stewart-Tolman experiment which examines the effect of inertia on moving charges.

BowlOfRed
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Interesting question. So initially , the electrons near the earth move faster than the electrons at the top . Hence , the current would be different initially. This is called a non -steady or transient state. Now consider any part of the wire. The number of electrons leaving that part from the bottom is more than the number of electrons entering from the top. This leads to a buildup of positive charges in that part , which attracts the incoming electrons from the top ( thus increasing their speed) and also attracts the outgoing electrons ( their speed decreases as the force is in the opposite direction of velocity). This leads to a increase in the incoming current and decrease in the outgoing current until they both become equal and there is no further accumulation of charge. This phenomenon occurs at every part of the wire leading to a constant steady value of current throughout the wire ( the current through any cross section of the wire is same). This is called the steady state . We normally don't talk about this in circuit analysis as the steady state is achieved in a very short period of time