# Electrical potential of a point that sits in the origin of the coordinate system

#### arhzz1

Joined Oct 21, 2020
39
Hello!

Calculate the potential of a point charge Q1 sitting in the coordination origin as a function of the distance r. Assume that for r = ∞
ϕ (r) = 0. What energy do you have to expend to transfer the charge Q2 beetwen any two points (A,B) from the charge Q1.

So what I've tried is this;

ϕ (r) = $-\int_0^r E * ds$

Now here I am missing the E so I've found this formula

$E = \frac{1}{4 * \pi * e0} * \frac{Q} {r^2}$

So I've still got the same issue. What is my r and what is my Q. Should I put Q as e = 1,6?

Does the fact that it is sitting in the spot 0,0 mean anything. Also r is confusing me, r should be the distance,between the two points. Now I havent found anywhere how to calculate this distance.

Some guidance would be great, thanks!

#### MrAl

Joined Jun 17, 2014
8,554
Hello,

'r' is a general distance variable.
Charge is measured in Coulombs C. A unit charge therefore is 1C.
1.6e-19 is the charge on one electron, not one unit of charge.

#### arhzz1

Joined Oct 21, 2020
39
Hello,

'r' is a general distance variable.
Charge is measured in Coulombs C. A unit charge therefore is 1C.
1.6e-19 is the charge on one electron, not one unit of charge.
Okay so i cannot put Q as 1,6e-19. My question still remains how do i get the general distnave variable (r)

#### Papabravo

Joined Feb 24, 2006
17,263
If you are sitting at ∞, you can approach the origin in any direction that you choose. Do you suppose there might be a strategic choice of direction, perhaps along one of the axes? Does the choice affect the result. Does setting Q = constant affect the result?

The integrand is dot product of 2 vectors. A dot product is not the same thing as multiplication. If E and ds are vectors, their dot product is a scaler.

#### arhzz1

Joined Oct 21, 2020
39
If you are sitting at ∞, you can approach the origin in any direction that you choose. Do you suppose there might be a strategic choice of direction, perhaps along one of the axes? Does the choice affect the result. Does setting Q = constant affect the result?

The integrand is dot product of 2 vectors. A dot product is not the same thing as multiplication. If E and ds are vectors, their dot product is a scaler.
Okay so I've talked to my professor, and I've been looking at the problem completly the wrong way. I was just susposed to show the formulas that are used to calculate Voltage etc.. All it took was a bit of math and integrals. Sorry for the hastle, thank you for the help anyways!

#### MaxMeyer

Joined Oct 26, 2020
6
As required by the literature, your equations are correct. Although it is worth double-checking to find E.