Calculating Electric Potential and Field for a Charged Disk

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SUMMARY

The discussion focuses on calculating the electric potential and electric field due to a charged disk with a surface charge density, denoted as σ, at a point P. The relevant equations provided are V(P) = (1/4πε₀)∫(σ/r)dA for potential and E(P) = (1/4πε₀)∫(σâ r/r²)dA for electric field. Participants expressed confusion regarding the integration process and the relationship between the variables, particularly concerning angles in the diagram. A step-by-step breakdown of the integration process and variable relationships is essential for solving the problem.

PREREQUISITES
  • Understanding of electric potential and electric field concepts
  • Familiarity with calculus, specifically integration techniques
  • Knowledge of surface charge density and its implications
  • Basic understanding of vector notation in physics
NEXT STEPS
  • Study the derivation of electric potential from continuous charge distributions
  • Learn about the integration of charge distributions in electrostatics
  • Explore the concept of surface charge density and its applications
  • Review vector calculus, particularly in relation to electric fields
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Students in physics, particularly those studying electromagnetism, as well as educators looking for problem-solving strategies related to electric fields and potentials from charge distributions.

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Homework Statement



2. a) Find the potential due to a continuous charge distribution of a disk with a surface charge, x, at point P.
b) Find the electric field for part A using: attached formula .

Diagram attached.

Homework Equations



attached.

The Attempt at a Solution


Well my first clue was to trying to relate the variables given in the problem and diagrams in relation to potential. I wasn't really able to figure out a way to do so.
 

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For part B, I thought of using the equation given and plugging in the variables from the diagram. However, the angles are confusing me. It would be great if someone could explain how to approach this problem and break it down into steps. Thank you! \begin{align}V(P) &= \frac{1}{4\pi\epsilon_0}\int\frac{\sigma}{r}\,dA\\E(P) &= \frac{1}{4\pi\epsilon_0}\int\frac{\sigma\mathbf{\hat{r}}}{r^2}\,dA\end{align}
 

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