Finding charge of a uniformly charged disk

[minase]

Along the axis of a uniformly charged disk, at a point 0.6 m from the center of the disk, the potential is 91.4 V and the magnitude of the electric field is 86.5 V/m; at a distance of 1.5 m, the potential is 46.8 V and the magnitude of the electric field is 27.0 V/m. Find the total charge residing on the disk.

I have both equation to finding the electric field and potential field for a uniform disk. There are two unknowns in the equation they are R and σ. Are they giving too much information?

 

[minase]

I have the two equations here how do I go about solving this. After substuiting E ,v and x for both equations I can divide the two equation by each other. Is there any easier way to do this. It is a homework problem I don't want to lose point please reply :)
$$E = 2k_e\pi\sigma(1-\frac{x}{\sqrt{x^2+R^2}})$$
$$V = 2k_e\pi\sigma\(x(\sqrt{1+\frac{R^2}{x^2}}-1)$$

 

[thomate1]

Based on the given information, it is indeed possible to determine the total charge residing on the disk. The equations for the electric field and potential for a uniformly charged disk involve the variables R (radius) and σ (surface charge density). However, with the given values of potential and electric field at two different distances from the center of the disk, we can set up a system of equations and solve for both R and σ. Once these values are known, the total charge on the disk can be calculated by multiplying the surface charge density by the area of the disk.

It is important to note that the given information assumes a uniform distribution of charge on the disk, meaning that the charge is evenly spread out over the entire surface. This is a simplification and in reality, charge is not always distributed uniformly. Additionally, the equations used to calculate the electric field and potential for a uniformly charged disk may not accurately represent the actual behavior of a real system. Therefore, it is important to consider the limitations and assumptions of the given information when using it to determine the total charge on the disk. Further experimentation and analysis may be necessary to confirm the accuracy of the calculated value.