Find Potential of Disk of Radius R, Charge Q w/ Equ 1

[Miike012]

I would like to know if there is a way of finding the Potential of a disk of radius R and charge Q with uniform charge distribution using Equ 1 instead of Equ 2?

Equ 1:
ΔV = -∫Edotdx rather than

Equ 2:
ΔV = ∫dU_{elec potential}

For Equ 1 I'm guessing that the equation would be of the form...

ΔV = -∫∫Ecos(∏/2)dA = -∫∫EdA = -∫∫Edxdy
And
Limits of int (X-Direction): -√(R² - y²) to √(R² - y²)
Limits of int (Y-Direction): -√(R² - x²) to √(R² - x²)

And E would be the EField of a disk...

 

[vela]

You can certainly integrate the E field to find the potential, but your attempt is wrong. It looks like you're confusing calculating the potential with calculating E.

To use equation 1, you need to have already found $\vec{E}$, and you'd calculate the line integral along any path C that runs from infinity to the point $\vec{r}$:
$$ V(\vec{r}) = -\int_C \vec{E}\cdot d\vec{x}.$$ To find $\vec{E}$, you'd calculate the contribution from each piece of the disk to the electric field at some point in space, and then integrate over the entire disk.

To use equation 2, you take a similar approach as you do when calculating $\vec{E}$. You calculate the contribution from each piece of the disk to the electric potential at some point in space, and then integrate over the entire disk. Calculating electric potential is a bit easier than calculating the field because the potential is a scalar quantity. You don't have to worry about summing vectors like you do when calculating the electric field.

 

[Miike012]

You can certainly integrate the E field to find the potential, but your attempt is wrong. It looks like you're confusing calculating the potential with calculating E.

To use equation 1, you need to have already found $\vec{E}$, and you'd calculate the line integral along any path C that runs from infinity to the point $\vec{r}$:
$$ V(\vec{r}) = -\int_C \vec{E}\cdot d\vec{x}.$$ To find $\vec{E}$, you'd calculate the contribution from each piece of the disk to the electric field at some point in space, and then integrate over the entire disk.

So equation 1 would be..

V = -∫E_diskdx and integrate from x_f = distance from point to disk and x_i = ∞. is that correct?

 

[vela]

Yes, basically.