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

• songoku
In summary: We would not say "between A and B there is a voltage of 12 volts" because there is no way to tell what 12 means in that context.In summary, the conversation is about the difference between electric potential and voltage. Electric potential difference between the surface of this sphere and a point far away is -144 volts.
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

songoku said:
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.

songoku
haruspex said:
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.

songoku
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.

songoku
Cutter Ketch said:
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.

songoku
haruspex said:
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.

songoku
@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?"

songoku
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.

songoku
haruspex said:
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.

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.

songoku
kuruman said:
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 VAB (means VA - VB) and the answer is different compared to VBA (which is the same as -VAB)

songoku said:
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 VAB (means VA - VB) and the answer is different compared to VBA (which is the same as -VAB)
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 VAB? If, for example, it is called the "difference between A and B", then we will be able to tie the mathematical VA - VB to the wording in English as understood by the questioner.

songoku
kuruman said:
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 VAB? If, for example, it is called the "difference between A and B", then we will be able to tie the mathematical VA - VB to the wording in English as understood by the questioner.
Sorry there is no such thing, the previous question directly asked to find VAB

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

songoku said:
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

## 1. What is potential difference?

Potential difference, also known as voltage, is the difference in electrical potential between two points in an electric field. It is measured in volts (V) and represents the amount of energy required to move a unit of charge from one point to another.

## 2. How is potential difference related to a sphere and a point far away?

In this context, potential difference refers to the difference in electrical potential between the surface of a sphere and a point far away from it. The potential difference is affected by the electric field strength and the distance between the two points.

## 3. What factors affect the potential difference between a sphere and a point far away?

The potential difference between a sphere and a point far away is affected by the magnitude and direction of the electric field, the distance between the two points, and the charge distribution on the sphere.

## 4. How is potential difference measured between a sphere and a point far away?

To measure the potential difference between a sphere and a point far away, an instrument called a voltmeter is used. The voltmeter measures the voltage between the two points and provides a numerical value in volts.

## 5. What is the significance of studying potential difference between a sphere and a point far away?

Understanding the potential difference between a sphere and a point far away is important in various fields of science and engineering, such as in the design of electrical systems and in studying the behavior of electric charges. It also helps us understand the concept of electric potential and its relationship with electric fields.

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