Potential difference between the surface of a sphere and a point far away

[songoku]

Homework Statement

A metallic sphere of radius 1.0 cm is charged with 1.0 x 10^9 electrons in air.
Which of the following is closest to the electric potential difference between
the surface of this sphere and a point far away?
a. 70 V
b. 140 V
c. - 70 V
d. - 140 V
e. 9 x 10^20 V

Relevant Equations

V = kQ/r

V at surface = k Q / r = 9 x 10⁹ x (1 x 10⁹ x (-1.6 x 10^-19) / (1 x 10^-2)

= - 144 V

V at a point far away = 0 V

From the sentence "electric potential difference between the surface of this sphere and a point far away" means that the question asks about V at surface minus V at far away so the answer is -144 V?

Thanks

 

[haruspex]

From the sentence "electric potential difference between the surface of this sphere and a point far away" means that the question asks about V at surface minus V at far away so the answer is -144 V?

A "difference" is a magnitude, so unsigned. The difference between 2 and 3 is the same as the difference between 3 and 2.

 

[Cutter Ketch]

A "difference" is a magnitude, so unsigned. The difference between 2 and 3 is the same as the difference between 3 and 2.

I’m not sure I agree. I agree that in this problem as stated it would be hard to determine which direction they might mean. I think that is more about the word “between” than any definition of potential difference. “between” doesn’t suggest a direction. However, looking around at various definitions of potential difference, it seems clear that it is just $V_A - V_B$ including the sign. I believe the term potential difference is used in many contexts where the direction is clear (started here ended there) and the sign is really important.

 

[Cutter Ketch]

With much less firm conviction, I would also suggest that there is a tendency (certainly not a firm connotation) for “between A and B” to mean start at A end at B which in this context would mean $V_B - V_A$. However, I realize that is trying to put meaning where there may not be much.

 

[haruspex]

With much less firm conviction, I would also suggest that there is a tendency (certainly not a firm connotation) for “between A and B” to mean start at A end at B which in this context would mean $V_B - V_A$. However, I realize that is trying to put meaning where there may not be much.

I cannot accept that. "Between" is symmetric, as in "distance between". So even if you wanted to say that "difference" could be used directionally, as in "difference from ... to" (which sounds strange to me... why not say e.g. "increase"?), the use of "between" here invalidates that.

 

[Cutter Ketch]

I cannot accept that. "Between" is symmetric, as in "distance between". So even if you wanted to say that "difference" could be used directionally, as in "difference from ... to" (which sounds strange to me... why not say e.g. "increase"?), the use of "between" here invalidates that.

I can definitely see that point of view and even more or less agree. However, I’ll try to explain what I meant.

If we were on a road trip together and I said “there are no good restaurants between Bakersfield and Barstow” you would expect me to list those in the order we will be passing them. You would find it weird if I said them backwards. If we weren’t on a road trip at the time, maybe that wouldn’t say anything about direction, but when an order exists and we say “between” we expect the first one to be listed first and the second one to be listed second. There is no explicit indication of order, but it’s a pretty consistent convention in the language. Almost everybody will almost always list the waypoints in order of arrival.

Again, language, not physics, and as usual completely debatable.

The problem here is that choosing the correct answer requires assuming an order, but none is explicitly stated. I was noting a tea leaf to suggest which way to jump.

 

[kuruman]

@haruspex's interpretation that the difference is the absolute value of one number minus the other makes sense in general and is the default interpretation of "difference between" unless there is a reason for it not to be so. I believe that there are two reasons for it not to be so in this particular example.

Reason 1 is that one of the numbers participating in the difference is the potential at its reference point. The reference value is always subtracted from the non-reference value because that's what "reference" means. Therefore the difference must be taken as $V(r)-V(\infty)$ and not the other way around.

Reason 2 is that "electric potential difference between" leaves room for ambiguity because there is a word for the magnitude of that difference, namely "voltage", which was not used. We say that "Ohm's Law states that the voltage across a resistor is equal to the product of the current through the resistor and the value of the resistance", that "the charge on the plates of a capacitor is equal to the capacitance multiplied by the voltage across the plates", "the voltage of a battery is 12 V" and so on. The problem, as posted by the @songoku, is equivalent to "Adam is at x = -8 m and Becky is at x = 0 m. What is the position difference between Adam and Becky?"

I cannot fathom the author's intent, but if I were to write this question and were expecting the positive difference as the correct answer, I would ask something like, "if the metallic sphere were part of a spherical capacitor with the outer shell very far away, what would be the capacitor voltage?"

 

[haruspex]

The - ahem - difference in our positions is that I have concentrated on what the question asks rather than second guessing what the questioner intended to ask. Agreed? Arguably, the latter is more helpful to @songoku.

 

[Cutter Ketch]

The - ahem - difference in our positions is that I have concentrated on what the question asks rather than second guessing what the questioner intended to ask. Agreed? Arguably, the latter is more helpful to @songoku.

Yes, agreed. Unfortunately the multiple choice answers have two of the answers repeated with opposite signs, so some sort of mind reading or coin flip will be required.

 

[kuruman]

Agreed. Perhaps @songoku who, in all likelihood, knows the questioner's milieu better than us can provide useful input based on lecture notes, textbook, previously worked examples, etc. Let's wait to see what @songoku has to say.

 

[songoku]

Agreed. Perhaps @songoku who, in all likelihood, knows the questioner's milieu better than us can provide useful input based on lecture notes, textbook, previously worked examples, etc. Let's wait to see what @songoku has to say.

Sorry there is no reference to answer this question based on lecture notes and textbook. I base my thinking on what I did previously in exercise about electrical circuit where the question asked V_AB (means V_A - V_B) and the answer is different compared to V_BA (which is the same as -V_AB)

 

[kuruman]

Sorry there is no reference to answer this question based on lecture notes and textbook. I base my thinking on what I did previously in exercise about electrical circuit where the question asked V_AB (means V_A - V_B) and the answer is different compared to V_BA (which is the same as -V_AB)

That is all good but the question you posted here is asking you in plain English words to find the difference between the solid sphere and infinity (far away). If it asked you to find $V_{\infty0}$ or $V_{0\infty}$, the answer would be easy in the context that the second subscript is what is subtracted from the first when you take the difference. So in the question on which you based your thinking is there language using plain English words that gives a name to V_AB? If, for example, it is called the "difference between A and B", then we will be able to tie the mathematical V_A - V_B to the wording in English as understood by the questioner.

 

[songoku]

That is all good but the question you posted here is asking you in plain English words to find the difference between the solid sphere and infinity (far away). If it asked you to find $V_{\infty0}$ or $V_{0\infty}$, the answer would be easy in the context that the second subscript is what is subtracted from the first when you take the difference. So in the question on which you based your thinking is there language using plain English words that gives a name to V_AB? If, for example, it is called the "difference between A and B", then we will be able to tie the mathematical V_A - V_B to the wording in English as understood by the questioner.

Sorry there is no such thing, the previous question directly asked to find V_AB

But more or less I understand about this question. The only problem is semantics.

Thank you very much for all the help haruspex, Cutter Ketch, kuruman

 

[alan123hk]

From the sentence "electric potential difference between the surface of this sphere and a point far away" means that the question asks about V at surface minus V at far away so the answer is -144 V?

The potential difference between points A and b is