Question about the integral used to calculate the voltage between two points

  • #1
lys04
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3
Homework Statement
If the voltage between two points is the negative integral from A to B of Edl, then in a given problem where it asks me to find the voltage between two points, how do I know which is A and which is B? Will both a negative and positive answer be accepted since its relative, like for example point A is +2V compared to B but B might be -2V compared to A?
Relevant Equations
negative integral from A to B of Edl
^^
 

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  • #2
"between" is symmetric. It does not imply a direction, so the answer would be a magnitude. But is that the word used in the question?
 
  • #3
My usage of the word voltage, with which some PF users disagree, is to denote the absolute value of the potential difference between two points. If I want to refer to a quantity that could be positive or negative, i use "the electrostatic potential difference between from A to B".

When one writes ##Q=CV## for a capacitor, ##V## is called the voltage across the capacitor and is assumed to be always positive.
 
  • #4
kuruman said:
"the electrostatic potential difference between from A to B"
Between? Did you mean "the electrostatic potential difference from A to B"?
 
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  • #5
haruspex said:
"between" is symmetric. It does not imply a direction, so the answer would be a magnitude. But is that the word used in the question?
No, I am just asking generally, it hasn't come up in a question. It just confused me tho. Does magnitude mean it's always positive?
 
  • #6
haruspex said:
Between? Did you mean "the electrostatic potential difference from A to B"?
Idk, I saw a question online that was like find the potential difference between A and B so I got confused.
1692315704787.png
 
  • #7
kuruman said:
My usage of the word voltage, with which some PF users disagree, is to denote the absolute value of the potential difference between two points. If I want to refer to a quantity that could be positive or negative, i use "the electrostatic potential difference between from A to B".

When one writes ##Q=CV## for a capacitor, ##V## is called the voltage across the capacitor and is assumed to be always positive.
:ok:That makes sense. Thanks.
 
  • #8
haruspex said:
Between? Did you mean "the electrostatic potential difference from A to B"?
That's what I meant. I crossed out the superfluous "between". Thanks for the catch.
lys04 said:
No, I am just asking generally, it hasn't come up in a question. It just confused me tho. Does magnitude mean it's always positive?
The question in @haruspex's post #4 was addressed to me. It was a typo that I fixed. Sorry about the confusion.
 
  • #9
But in circuit analysis you have to get the sign of the potential difference right. All these sign problems usually go away when you remember, how the corresponding quantities are derived from Maxwell's equations.
 
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Related to Question about the integral used to calculate the voltage between two points

What is the integral used to calculate the voltage between two points?

The integral used to calculate the voltage (V) between two points A and B in an electric field (E) is given by the line integral: \( V = -\int_A^B \mathbf{E} \cdot d\mathbf{l} \). This integral represents the work done per unit charge in moving a test charge from point A to point B.

Why is there a negative sign in the voltage integral?

The negative sign in the voltage integral \( V = -\int_A^B \mathbf{E} \cdot d\mathbf{l} \) indicates that the voltage is defined as the work done against the electric field. It ensures that the potential decreases in the direction of the electric field.

How do you choose the path for the line integral when calculating voltage?

The path chosen for the line integral can be any path connecting points A and B because the electric field is a conservative field. The voltage between two points is path-independent and depends only on the endpoints A and B.

Can the integral be used in non-uniform electric fields?

Yes, the integral \( V = -\int_A^B \mathbf{E} \cdot d\mathbf{l} \) can be used in both uniform and non-uniform electric fields. In non-uniform fields, the electric field \(\mathbf{E}\) varies along the path, and the integral accounts for these variations.

What is the physical significance of the voltage calculated using this integral?

The voltage calculated using the integral represents the electric potential difference between two points. It quantifies the work done per unit charge to move a test charge from one point to another in the presence of an electric field.

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