How Do You Verify Electrostatic Force via Direct Integration?

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SUMMARY

The discussion focuses on verifying the electrostatic force equation F = qE = -q²/(16πε₀d²) through direct integration. The challenge involves integrating the surface charge density σ_f(y,z) = -qd/(2π(d²+y²+z²)^(3/2)) to confirm the resultant Coulomb force between charge q and the induced charge. Participants express uncertainty about whether to integrate the surface charge density or the force itself, indicating a need for clarity in the problem's requirements.

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  • Understanding of electrostatics and Coulomb's law
  • Familiarity with surface charge density concepts
  • Knowledge of electric potential and its relation to electric fields
  • Proficiency in calculus, specifically integration techniques
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  • Learn about surface charge density and its implications in electrostatics
  • Explore the relationship between electric potential and electric fields
  • Practice integration techniques relevant to physics problems
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This discussion is beneficial for physics students, educators, and anyone involved in electrostatics or electrical engineering, particularly those interested in the mathematical verification of electrostatic forces.

Midas_Touch
The problem says

Verify by direct integration that

F= qE = - q^2/(16*pi*epsilon_0*d^2) in the "x unit" direction

is the resultant of the Coloumb force between q and the induced charge described by

sigma_f(y,z) = -qd/(2*pi*(d^2+y^2+z^2)^3/2

-------------

Okay, I am not sure what to integrate here. Do I integrate the surface charge density or the force?

Thank you,
Midas
 
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F = -dU and -(grad V) = E so maybe your suppose to verify electric potential by integrating qE along x. I'm not sure exactly what they are asking for either...
 
Please note that the OP is nearly 5 yrs old. I would assume this homework problem has long neen resolved.

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