# Understanding the Concept of Infinity as a Reference in Physics: Explained

• B
In summary, the concept of using "infinity" as a reference point in physics is often just a convenient convention. It is simply a point far enough away that going any further would make a negligible difference to the system. In terms of calculating the voltage of a point charge, it is defined as the difference in electric potential, with one possible definition being U = (Q/4pi*e_0*r), where r is the distance from the charge and the function tends to 0 as r approaches infinity. However, this does not necessarily use infinity as a reference point, as an arbitrary constant can be added to the potential without changing the physics.
I'm facing a problem in my physics course which is accepting that infinity can be a reference point in both Electrostatics (calculating the voltage of a point) and Matter Properties (calculating the gravitational potential energy), how come we use a reference point which we don't know where it is, keep in mind that I don't have any problems dealing with infinity when we plug it in a mathematical relation, what I want is to understand the physical concept of choosing infinity as a reference.

hsdrop
I want is to understand the physical concept of choosing infinity as a reference.
There is no general physical concept. It's often just a convenient convention

I'm facing a problem in my physics course which is accepting that infinity can be a reference point in both Electrostatics (calculating the voltage of a point) and Matter Properties (calculating the gravitational potential energy), how come we use a reference point which we don't know where it is, keep in mind that I don't have any problems dealing with infinity when we plug it in a mathematical relation, what I want is to understand the physical concept of choosing infinity as a reference.

"A point at infinity" is simply a point far enough away that going any further would make a negligible difference to the system. E.g. the point at infinity is far enough away that the potential energy is a maximum (for GPE or attractive charges) or a minimum (for repulsive charges).

A.T. said:
There is no general physical concept. It's often just a convenient convention
Ok then, I can't get over that "convenient convention", and please tell me, what makes it legit ?

PeroK said:
"A point at infinity" is simply a point far enough away that going any further would make a negligible difference to the system. E.g. the point at infinity is far enough away that the potential energy is a maximum (for GPE or attractive charges) or a minimum (for repulsive charges).
Thanks for your reply, but can you tell me how we are able to calculate for instance the voltage of a point charge having a charge Q, it's coordinates are (X,Y) while setting our reference point as infinity ?

Thanks for your reply, but can you tell me how we are able to calculate for instance the voltage of a point charge having a charge Q, it's coordinates are (X,Y) while setting our reference point as infinity ?

Voltage is the difference in electric potential, so the question is how to define electric potential. One definition of electric potential for a point charge ##Q## is:

##U = \frac{Q}{4\pi \epsilon_0 r} \ ##, where ##r## is the distance from the charge.

This gives a function of ##r## that tends to ##0## as ##r \rightarrow \infty##. And, in many ways, this is the most natural and useful definition, given the relationship between ##U## and ##r##. I'm not sure I would say this uses ##\infty## as a reference point, though.

You could equally well define:

##U = U_0 + \frac{Q}{4\pi \epsilon_0 r} \ ##, where ##U_0## is some constant.

If ##Q## is negative (or if ##Q## is positive and ##U_0## is negative), you will have some radius ##r_0## where ##U(r_0) = 0##. But, it's not really making ##r_0## special.

PS How you define ##U(r)## doesn't change the critical fact that the function ##U(r)## never attains its max or min, but tends to one of these as ##r \rightarrow 0## and the other as ##r \rightarrow \infty##. In a sense, ##r \rightarrow \infty## has a physical meaning whether you like it or not!

how come we use a reference point which we don't know where it is
This might be the core of your confusion: We aren't using the position as reference, just the finite value at which some function converges.

PeroK said:
Voltage is the difference in electric potential, so the question is how to define electric potential. One definition of electric potential for a point charge ##Q## is:

##U = \frac{Q}{4\pi \epsilon_0 r} \ ##, where ##r## is the distance from the charge.

This gives a function of ##r## that tends to ##0## as ##r \rightarrow \infty##. And, in many ways, this is the most natural and useful definition, given the relationship between ##U## and ##r##. I'm not sure I would say this uses ##\infty## as a reference point, though.

You could equally well define:

##U = U_0 + \frac{Q}{4\pi \epsilon_0 r} \ ##, where ##U_0## is some constant.

If ##Q## is negative (or if ##Q## is positive and ##U_0## is negative), you will have some radius ##r_0## where ##U(r_0) = 0##. But, it's not really making ##r_0## special.
Hello. Why are we giving it an arbitrary constant in the first place?

PeroK said:
Voltage is the difference in electric potential, so the question is how to define electric potential. One definition of electric potential for a point charge ##Q## is:

##U = \frac{Q}{4\pi \epsilon_0 r} \ ##, where ##r## is the distance from the charge.

This gives a function of ##r## that tends to ##0## as ##r \rightarrow \infty##. And, in many ways, this is the most natural and useful definition, given the relationship between ##U## and ##r##. I'm not sure I would say this uses ##\infty## as a reference point, though.

You could equally well define:

##U = U_0 + \frac{Q}{4\pi \epsilon_0 r} \ ##, where ##U_0## is some constant.

If ##Q## is negative (or if ##Q## is positive and ##U_0## is negative), you will have some radius ##r_0## where ##U(r_0) = 0##. But, it's not really making ##r_0## special.
Hello. Why do we use the arbitrary constant may I ask? What function does it serve? Is it the initial electric potential at that reference point?

ayans2495 said:
Hello. Why do we use the arbitrary constant may I ask? What function does it serve? Is it the initial electric potential at that reference point?
Mathematically, the potential when differentiated gives the electric field. And an anti-derivative has an arbitrary constant.

Physically, only the difference in potential is important, so you can add a constant without changing the physics. And, yes, this is equivalent to choosing a certain reference point as having zero potential.

vanhees71
ayans2495 said:
Hello. Why do we use the arbitrary constant may I ask? What function does it serve? Is it the initial electric potential at that reference point?
None. That's an important point. The electrostatic potential is only determined up to an arbitrary additive constant without any physical significance. Only potential differences are related to physical observables. That's why you can choose the additive constant arbitrarily, and it is usually convenient to choose it such that the potential goes to zero at infinity.

I'm facing a problem in my physics course which is accepting that infinity can be a reference point in both Electrostatics (calculating the voltage of a point) and Matter Properties (calculating the gravitational potential energy), how come we use a reference point which we don't know where it is, keep in mind that I don't have any problems dealing with infinity when we plug it in a mathematical relation, what I want is to understand the physical concept of choosing infinity as a reference.
It's a reference for theorists, not for experimentalists. We cannot measure at infinity, but we can put ##r\to \infty## in equations.

vanhees71
We cannot measure the absolute electric potential anyway, as stressed above, but only potential differences ("voltages") between two points separated by a finite distance in the lab. So theory and experiment are in no contradiction here but perfectly match (as it should be)!

Demystifier

## 1. What is the concept of infinity in physics?

The concept of infinity in physics refers to the idea of a quantity or value that is limitless or unbounded. It is a theoretical concept that is used to describe phenomena that have no defined endpoint or boundary.

## 2. How is infinity used as a reference in physics?

Infinity is often used as a reference point in physics to describe the behavior of systems or objects at the extreme ends of a spectrum. For example, in thermodynamics, infinity is used to describe the behavior of a system in the limit of infinite temperature or pressure.

## 3. What are some examples of infinity in physics?

Some examples of infinity in physics include the concept of infinite energy in black holes, infinite density at the center of a singularity, and the infinite expansion of the universe in the Big Bang theory.

## 4. How is the concept of infinity dealt with in mathematical equations?

In mathematics, infinity is often represented by the symbol ∞ and is used in equations to indicate that a value is unbounded or approaching an unbounded quantity. It is also used in calculus to describe limits and infinite series.

## 5. Why is understanding the concept of infinity important in physics?

Understanding infinity is important in physics because it allows us to describe and make predictions about phenomena that have no defined endpoint or boundary. It also helps us understand the behavior of systems at extreme values, which can be crucial in many areas of physics such as cosmology and thermodynamics.

• Topology and Analysis
Replies
2
Views
466
• Classical Physics
Replies
86
Views
4K
• Classical Physics
Replies
1
Views
753
• Classical Physics
Replies
6
Views
816
• Classical Physics
Replies
15
Views
730
• Classical Physics
Replies
7
Views
1K
• Electromagnetism
Replies
8
Views
999
• Classical Physics
Replies
7
Views
1K
• Classical Physics
Replies
1
Views
598
• Classical Physics
Replies
1
Views
758