What is taken as datum level for the following absolute potentials?

[tellmesomething]

Homework Statement

Title

Relevant Equations

None

We take out "formulas" for electric potential from the relation

$$V=\int E.dx$$

Some general formulas are :
For a hollow sphere : $\frac{Q} {4π\epsilon_0 x}$ when x>R, x =distance of that point from the center

And the problem is we just input the distance in sums to calculate absolute electric potential even..
Here its clear if I take datum level as ∞ I get potential as 0. All good

Consider this next potnetial

Potential on the axis of a disc is

$$\frac{\sigma √(R²+z²)} {2\epsilon_0}$$
Where z is the distance from the center of the disc on its axis of symmetry.

What do we take datum level here?

 

[kuruman]

By datum level, I assume that you mean the reference point of the potential at which it is zero.

First of all the expression for the potential function as derived from the electric field is not what you have but $$V(\mathbf r)=-\int_{\mathbf r_{\text{ref}}}^{\mathbf r } \mathbf{E}\cdot d\mathbf r$$where $\mathbf r_{\text{ref}}$ is the point where the potential is taken to be zero.

The book/website/lecture notes where you got this expression probably says where the assumed zero of potential is.

 

[tellmesomething]

By datum level, I assume that you mean the reference point of the potential at which it is zero.

First of all the expression for the potential function as derived from the electric field is not what you have but $$V(\mathbf r)=-\int_{\mathbf r_{\text{ref}}}^{\mathbf r } \mathbf{E}\cdot d\mathbf r$$where $\mathbf r_{\text{ref}}$ is the point where the potential is taken to be zero.

The book/website/lecture notes where you got this expression probably says where the assumed zero of potential is.

It was in a random problems set, the exact question being " A part of disc of radius R and angle π/6 carries uniformly distributed charge of density $\sigma$. Electric potential at the centre of the disc is:

I mindlessly used the above derived formula and got the answer which matches the answer given I.e $\frac{\sigma R}{24\epsilon_0}$ . I believe the question asks to find the absolute potential and also has not given us any hint to infer Where the reference level is.. So isnt this answer wrong?