Finding charge of a uniformly charged disk

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SUMMARY

The discussion focuses on calculating the total charge on a uniformly charged disk using the electric field and potential equations. At a distance of 0.6 m from the center, the potential is 91.4 V and the electric field is 86.5 V/m; at 1.5 m, the potential is 46.8 V and the electric field is 27.0 V/m. The user is attempting to solve for the unknowns, the radius (R) and surface charge density (σ), using the equations E = 2k_eπσ(1 - x/√(x² + R²)) and V = 2k_eπσ(x(√(1 + R²/x²) - 1)). They seek a more straightforward method for solving these equations.

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  • Understanding of electric fields and potentials in electrostatics
  • Familiarity with the equations for electric field and potential of a uniformly charged disk
  • Knowledge of algebraic manipulation and substitution methods
  • Basic grasp of calculus concepts related to limits and continuity
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  • Study the derivation of electric field equations for charged disks
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  • Explore numerical methods for approximating solutions to complex equations
  • Investigate the impact of varying disk radius on electric field and potential
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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?
 
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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)
 
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