Surface charge, electric fields, and capacitance

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SUMMARY

This discussion focuses on the electric field and capacitance of two large conducting sheets with positive surface charge density. When one sheet is shrunk to a square with sides equal to the distance d between them, the electric field at the central axis of the smaller sheet is affected by the change in geometry. Additionally, the relationship between electric fields E1 and E2 in series and parallel configurations with dielectrics K1 and K2 is analyzed. The equivalent capacitance for both configurations is derived using the formula C = (K*Epsilon*Area)/d.

PREREQUISITES
  • Understanding of electric fields from surface charges
  • Familiarity with capacitance formulas and concepts
  • Knowledge of dielectric materials and their properties
  • Basic calculus for integrating electric field equations
NEXT STEPS
  • Study the effects of geometry on electric fields in capacitors
  • Learn about the behavior of dielectrics in electric fields
  • Explore the derivation of capacitance in series and parallel configurations
  • Investigate the integral calculus involved in electric field calculations
USEFUL FOR

Physics students, electrical engineers, and anyone studying electrostatics and capacitor design will benefit from this discussion.

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Homework Statement


Two large conducting sheets are charged with a positive surface charge density. They stand vertically facing each other a distance d apart.

a.) suddenly, we shrink the left sheet to a square with sides equal to d, what is the field at the point along the central axis of the smaller sheet a point directly between the two plates?

b.) By shrinking both sheets to a square with sides equal to d, let each sheet have oppositely charged sufaces with two dielectrics (K1, K2). what is the relationship between E1 and E2 for a series configuration?

c.) Alternatively for b) what is the E-Field relationship for a parallel configuration when the sheet's contact area is shared equally?

d.) what is the equivalent capacitance in each case b) c)?



Homework Equations



C = (K*Epsilon*Area)/d

Efield at a point from a surface charge is = integral of kq/r^2 dq

dq = sigma dA

The Attempt at a Solution



I don't really know where to begin with this...I know in between two parallel plate capacitors the field is uniform and it will change with the change in one plate but the question does not explain what the original dimensions are...and when one shrinks that means the field won't be uniform...

But how do I figure out exactly what that is?
 
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I want to take this one step at a time so I want to address A.) first
 

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