Find surface area of a non-conducting sheet

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SUMMARY

The discussion focuses on calculating the surface charge density (σ) of a large charged non-conducting sheet in relation to a small sphere of mass m and charge q, which hangs at an angle θ from a silk thread. The electric field (E) of the sheet is expressed as E = σA/ε, where ε represents the permittivity of free space. The relationship between the electric field of the sphere and the electric field of the sheet is crucial for determining σ. The solution involves setting up an integral with circular elements and relating the total force normal to the plane to the angle θ.

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  • Understanding of electric fields and forces in electrostatics
  • Familiarity with surface charge density concepts
  • Knowledge of integral calculus for setting up electric field calculations
  • Basic principles of trigonometry as applied to angles and forces
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  • Study the derivation of electric field equations for charged sheets
  • Learn about the relationship between charge density and electric field strength
  • Explore integral calculus applications in electrostatics
  • Investigate the effects of angle θ on forces in electrostatic systems
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Students and educators in physics, particularly those focusing on electrostatics and electric fields, as well as anyone involved in solving problems related to charge distributions and forces on charged objects.

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Homework Statement



A small sphere of mass m carries a charge of q. It hangs from a silk thread which makes an angle
θ with a large charged non-conducting sheet. Calculate the surface charge density on the sheet.



Homework Equations


∫E.ds


The Attempt at a Solution


I found E of the sheet to be E = σA/ε

how do i find find σ, surface charge density for this problem what is the relationship between E of the sphere and E of the sheet?
 
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Well, I'd think about setting up an integral with circular elements, each centered on the point on the sheet closest to the ball. Each point on one of these circles will have the same force on the ball in the direction normal to the sheet. I believe the force would fall off linearly with increasing radius - increasing circle circumference linearly balanced against the inverse-square field fall-off, but the progressively increasing angles from normal-to-the-plane directly under to the ball to parallel to the sheet at infinity would give a trig term I'm too lazy to figure out. (I'm assuming the sheet is vertical. Wouldn't the length of the thread and the distance of the thread's upper suspension point from the sheet need to be given? Otherwise you could get any angle of the thread even with the ball touching the sheet. ) You'll need the equation relating total force normal to the plane to theta. Then relate charge density to force, substitute and solve.
 

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