Hallow I found it very difficult to understand why the calculation

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Discussion Overview

The discussion revolves around the differences in calculating the capacitance of various capacitor geometries, specifically parallel plate, cylindrical, and spherical capacitors. Participants explore the underlying electric field contributions in each configuration and how these affect capacitance calculations.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant expresses confusion over why the calculation for capacitance differs between parallel plate capacitors and spherical or cylindrical capacitors, noting that the electric field in parallel plates is considered as a resultant from both plates.
  • Another participant prompts a consideration of the electric field within a hollow spherical conductor carrying a charge, suggesting a different perspective on field contributions.
  • A participant argues that for all three configurations, the electric field can be determined by adding contributions from each plate, but notes that in cylindrical and spherical configurations, the outer plate does not contribute to the field between the plates.
  • One participant reiterates their confusion, questioning why both charges are present in all capacitors yet the geometries yield different results, emphasizing the unique arrangement of conductors in cylindrical and spherical capacitors compared to parallel plates.
  • Another participant reinforces this point by highlighting that in cylindrical and spherical capacitors, one conductor encloses another, which is not the case in parallel plate capacitors.

Areas of Agreement / Disagreement

Participants express differing views on the contributions of electric fields in various capacitor geometries, with no consensus reached on the underlying reasons for the differences in capacitance calculations.

Contextual Notes

Participants have not fully resolved the assumptions regarding electric field contributions and the implications of conductor arrangements in different capacitor types.

Godwin Kessy
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Hallow! I found it very difficult to understand why the calculation

Hallow! I found it very difficult to understand why the calculation for deducing the capacitance of the parallel plate capacitor differs from that of spherical and cylindrical capacitor...
In the sense that, the electric field in parallel plate capacitor is obtained as a resultant of the electric field due each capacitor..IE. The electric field is twice that produced by each plate... But for spherical and cylindrical capacitor the electric field used to obtain the potential difference across the surfaces and hence the capacitance, is as if only one surface is responsible for the electric field...
Now which is which...??
Personally am comfortable with using the electric field as the resultant of two fields from each surface.. Based on coulombs law of static electricity...
 
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Ask yourself: What's the field within the cavity of a hollow spherical conductor that carries a charge?
 


My point is this: For all three configurations--parallel plate, cylindrical, and spherical--you can always find the field between the plates by adding the contribution from each plate. But in the latter two configurations, the outer plate contributes nothing.
 


Now that's what confusing, see this, in all capacitors both charges, positive and negative are present, what's makes the other geometries different to the parallel plate?
 


Godwin Kessy said:
Now that's what confusing, see this, in all capacitors both charges, positive and negative are present, what's makes the other geometries different to the parallel plate?
In the cylindrical and spherical capacitors, one conductor encloses the other. Not so in the parallel plate arrangement.
 

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