# B Infinity as a reference.

1. Dec 20, 2016

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.

2. Dec 20, 2016

### A.T.

There is no general physical concept. It's often just a convenient convention

3. Dec 20, 2016

### PeroK

"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).

4. Dec 20, 2016

Ok then, I can't get over that "convenient convention", and please tell me, what makes it legit ?

5. Dec 20, 2016

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 ?

6. Dec 20, 2016

### PeroK

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.

7. Dec 20, 2016

### PeroK

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!

8. Dec 20, 2016

### A.T.

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.