Electric Potential Between Two Charges

[maw524]

Homework Statement

I have a series of questions regarding electric potential at various points in space given various point charges. The one that would probably be best to focus on is a charge of +q and a second charge of -2q a distance "d" further along the x-axis, find the non-infinity points at which the electric potential due to the charges is zero.

The method isn't actually the issue, I can get a numerical answer. However: I have absolutely no idea what it means, conceptually. How can a positive test charge have no potential energy at some point between these charges? What is actually happening at the point between them at which the potential is zero? Why is there a point of zero potential to the left of the positive charge, one in between the two, but no point of zero potential to the right of the negative charge?

Homework Equations

V=kq/r

The Attempt at a Solution

As for why I don't understand:

With electric potential being thought of as the energy per charge at a point in space, I don't see how there can be a point between the two charges (considering that they are oppositely charged) at which any possible test charge would not have some potential energy. A positive placed anywhere between them would be pulled right toward the negative charge and have positive potential energy, and a negative charge placed anywhere between them would be pushed left toward the positive charge, and so would have negative potential energy (assuming left is negative).

As for looking at the electric potential as the energy used to bring a charge from infinity to that point, I, frankly, don't understand how that works with negative source charges. The further away from a negative source charge, the more potential energy a positive test charge would have. How does no potential at infinity work? At what point does its potential stop increasing and begin decreasing to zero. And how does the "bringing charges in from infinity" work with a charge placed between these two producing zero potential?

 

[tiny-tim]

welcome to pf!

hi maw524! welcome to pf!

… I have absolutely no idea what it means, conceptually. How can a positive test charge have no potential energy at some point between these charges? What is actually happening at the point between them at which the potential is zero? Why is there a point of zero potential to the left of the positive charge, one in between the two, but no point of zero potential to the right of the negative charge?
…
With electric potential being thought of as the energy per charge at a point in space, I don't see how there can be a point between the two charges (considering that they are oppositely charged) at which any possible test charge would not have some potential energy. A positive placed anywhere between them would be pulled right toward the negative charge and have positive potential energy, and a negative charge placed anywhere between them would be pushed left toward the positive charge, and so would have negative potential energy (assuming left is negative).

zero potential doesn't really mean anything conceptually, it's an arbitrary concept of there being zero work done in moving the charge there from infinity …

and potential (or potential energy) has nothing to do with how a charge is pushed: that depends only on the gradient of the potential

 

[maw524]

Okay, so arbitrary how, exactly? Arbitrary like selected reference points vs other relative reference points?

It still means something though. V=U/q so in other words, the amount of potential energy per charge at that point in space. So how can there be a point between them with zero potential energy? It'd be like one planet and then a second planet twice as big and the first one has...negative gravity (not exactly a real-world analogy, but hopefully you get my point). At any point between the two, the small planet's oppo-gravity would give potential energy due to its push, and the big planet would provide negative potential because of it's even bigger pull.

To me, V=U/q seems like, going back to normal gravity for this analogy, the potential energy due to gravity, U=mgh, being viewed without a value for mass, and so in other words, "gh" per unit of mass. In this case, V is equivalent to "gh".

Just as "gh" would give a us a number representing the Joules of potential energy per kilogram placed at that height, so does "V" give us the number of Joules per charge placed at that point in space. How can there be a point between them where "V" is zero?

 

[Dadface]

Hello maw.If a test charge is at a point where the potential is zero that doesn't mean that the potential energy is zero.

 

[tiny-tim]

hi maw524!

Okay, so arbitrary how, exactly? Arbitrary like selected reference points vs other relative reference points?

yes, arbitrary like any reference point

It still means something though. V=U/q so in other words, the amount of potential energy per charge at that point in space…

yes, but V and U use the same arbitrary reference point

To me, V=U/q seems like, going back to normal gravity for this analogy, the potential energy due to gravity, U=mgh, being viewed without a value for mass, and so in other words, "gh" per unit of mass. In this case, V is equivalent to "gh".

Just as "gh" would give a us a number representing the Joules of potential energy per kilogram placed at that height, so does "V" give us the number of Joules per charge placed at that point in space. How can there be a point between them where "V" is zero?

but with gravity, h = 0 is the arbitrary level that happens to be chosen for the particular diagram …

V gives the number of joules (small "j", btw, if you write it in full ) for the work needed to get it to that point from the arbitrary reference level

Hello maw.If a test charge is at a point where the potential is zero that doesn't mean that the potential energy is zero.

well, yes it does … using that particular reference level for energy, the PE is zero

 

[Dadface]

Potential and potential energy are different things.If the potential at a point is zero then the the potential energy will be zero but only between that point and any other point or points where the potential is zero.