Moving Point Charges - Voltage Calculations

[somasimple]

Hi all,

Here is my problem:

Two positive points charges are situated as the initial figure:
1/ How to compute the voltage between A and B (or C)?

2/ If the final condition is like described in the second figure, what is now the voltage between A and B.
3/ if the transition between the two states takes a time t1, does the speed of this transition changes something about the voltage that exists between A and B?

Thanks.

 

[Redbelly98]

What is the potential or voltage due to a single point charge? That would be useful here.

 

[somasimple]

I have some notions that come from this page:
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/potpoi.html
and that one
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/mulpoi.html#c1

But since there is a space behind charges I suppose the computation a little different?

 

[somasimple]

BTW, I received a warning/infraction but I'm not an undergrad student.
The question is just outside my level of expertise (health).

 

[Redbelly98]

. . . and that one
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/mulpoi.html#c1

Yes, exactly, that is the way to go.

But since there is a space behind charges I suppose the computation a little different?

No, it's really the same computation. Use the distance from the point of interest (either A or B) to each charge.

BTW, I received a warning/infraction but I'm not an undergrad student.
The question is just outside my level of expertise (health).

Okay, but that is not relevant. Any textbook-style problem, even if it's for your own independent study, is subject to our "homework help" rules. If you haven't already, you can check out our policy by clicking the "Rules" link at the top of this page, and then scroll down to the section titled Homework Help.

 

[somasimple]

Okay, but that is not relevant. Any textbook-style problem, even if it's for your own independent study, is subject to our "homework help" rules. If you haven't already, you can check out our policy by clicking the "Rules" link at the top of this page, and then scroll down to the section titled Homework Help.

I made the subject. I made the images. I put the subject in the right forum (Classics Physics) but the subject was moved by a moderator.

 

[Redbelly98]

If you'd like to continue with working on the problem, I am willing to help.

As a start, I can suggest computing the potential at point B in your first figure.

 

[somasimple]

As a start, I can suggest computing the potential at point B in your first figure.

My shortcut (?)
k = coulomb's constant
d₂ = d-r₂
V_AB=(k*q₁/(r₁+d₂))+(k*q₂/(r₂+d₂))
it takes account of the space behind the charges (?)

 

[Redbelly98]

Ah, no, it doesn't really work that way. For example, the potential at point B due to charge q1 alone would be

k q₁ / (distance from q₁ to B)​

However, I am looking at the figures more closely and some things are confusing me:

1. You have used r₂ to refer to the position of q₁. Did you mean to mix the subscripts like that? It is confusing to do so, but we can go with that definition if that is what you intend.

2. Do "A" and "B" refer to points along the line joining the charges? It would make sense if they do, but then point "C" would be the same as point "B" in your first figure.

 

[somasimple]

there is an error in the figure. r₁ was meant to belong to q₁.
and r₂ to q₂.

 

[somasimple]

2. Do "A" and "B" refer to points along the line joining the charges? It would make sense if they do, but then point "C" would be the same as point "B" in your first figure.

Yes.

 

[Redbelly98]

Okay, thanks.

So, if you just had charge q1, the potential at B would be

k q₁ / r₁​

But you also need to add the potential due to charge q2, so you'd have

V_B = (k q₁ / r₁) + ____​

Then you'd do the same thing for V_A, the potential at point A.

 

[somasimple]

VB = (k q1 / r1) + (k q2 / r2)
VA = (k q1 /(d-r1)) + (k q2 /(d- r2)) ?

 

[Redbelly98]

Yes, that's right.

And the voltage between A & B would be V_A-V_B ... or V_B-V_A, depending on whether A or B is being used as the reference point.

EDIT:
Your question #2 works the same way.
#3: As long as we are ignoring relativistic effects, then no, the speed of the transition does not affect the potential.

 

[somasimple]

#3: As long as we are ignoring relativistic effects, then no, the speed of the transition does not affect the potential.

Does it affect the electric current?

 

[Redbelly98]

What current?

 

[somasimple]

I thought there was a current since there is a voltage but and I'm certainly wrong.

 

[somasimple]

I made new pictures:
Hope they are more accurate.

 

[Redbelly98]

I thought there was a current since there is a voltage but and I'm certainly wrong.

There would have to be some type of conductor joining A and B for there to be a current.

I made new pictures:
Hope they are more accurate.

Looks good, that more accurately depicts the situation you are describing.

 

[somasimple]

There would have to be some type of conductor joining A and B for there to be a current.

That is what I learned some time ago. A current may exist only if there is an electric circuit.

Looks good, that more accurately depicts the situation you are describing.

Thanks.