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# Surface Integral watch

1. I want to estimate the energy of point charges over a sphere, however I think I am doing the integral wrong.

I know the energy is calculated by:

Where pi are the position vectors and qi are the charges of the points. Since the charge I am taking is one, and the radius of my sphere is one, when I model the point charges as a uniform charge over the sphere I can get the energy to be:

and then taking polar coordinates I get and fixing as I get:

which cancels to:

However I know it should be , what am I doing wrong??
However I know it should be , what am I doing wrong??
So you're out by a factor of 4pi, which happens to be the surface area of a sphere of radius 1. So, do you need to take charge density into account? Not that I know anything about this.
3. (Original post by ghostwalker)
So you're out by a factor of 4pi, which happens to be the surface area of a sphere of radius 1. So, do you need to take charge density into account? Not that I know anything about this.
I did realise that I was out by the surface area which made me think I was doing it slightly wrong but am definitely close. I shall look into the charge density so thanks you for that.

I am unsure of my notation as well however, I am not sure if it should in fact be:

?
I did realise that I was out by the surface area which made me think I was doing it slightly wrong but am definitely close. I shall look into the charge density so thanks you for that.

I am unsure of my notation as well however, I am not sure if it should in fact be:

?
I would have thought:

?
5. (Original post by ghostwalker)
I would have thought:

?
I think it's because I have fixed the point and when I do this I must multiply by the surface area of the sphere. Which sorts my original issue. I shall look into notation and post again when I have an answer. I would agree with you though, it seems I wasn't understanding the notation when I took the notes back in November!
6. Ok so I think it goes as follows:

...
One thing I would query, is why you have the 16/pi^2 to start with - but I'm not up on the physics behind this.
8. (Original post by ghostwalker)
One thing I would query, is why you have the 16/pi^2 to start with - but I'm not up on the physics behind this.
Sorry, I have found that is the charge density I am not up on the physics of it either to be honest, I need to look into it more, but at least I know where I was going wrong now, thanks for the help, always useful to bounce ideas around!

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