Surface charge density and more, for a parallel plate cap.

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SUMMARY

The discussion centers on calculating the electric field, surface charge density, and capacitance of an air-filled parallel plate capacitor with an area of 7.60 cm² and a separation of 1.60 mm under a 25.0 V potential difference. The electric field was correctly calculated as 15625 N/C. However, the surface charge density was incorrectly computed, leading to a value of 5.84795 nC/m², which was significantly off. The capacitance was also miscalculated as 47500000 pF, indicating a misunderstanding of the relevant equations and constants, particularly the permittivity of free space (ε₀).

PREREQUISITES
  • Understanding of electric fields and potential difference
  • Familiarity with capacitance formulas, specifically C = ε₀ * A / d
  • Knowledge of surface charge density calculations, Q/A
  • Basic grasp of the permittivity of free space (ε₀) and its value (approximately 8.85 x 10⁻¹² F/m)
NEXT STEPS
  • Review the concept of electric field calculations in capacitors
  • Study the derivation and application of the capacitance formula C = ε₀ * A / d
  • Learn about surface charge density and its relationship with capacitance and voltage
  • Investigate the significance of the permittivity of free space (ε₀) in electrostatics
USEFUL FOR

Students studying electromagnetism, physics educators, and anyone seeking to understand the principles of capacitors and electric fields in parallel plate configurations.

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Homework Statement


An air-filled capacitor consists of two parallel plates, each with an area of 7.60 cm2, separated by a distance of 1.60 mm.
1. If a 25.0 V potential difference is applied to these plates, calculate the electric field between the plates.
2. What is the surface charge density?
3. What is the capacitance?

Homework Equations


field=kq/(r^2)
V=kq/r
so q = Vr/k

The Attempt at a Solution


1. field=kVr/kr^2=V/r=25/.0016=15625N/C (correct)
2. q/A=Vr/kA=25(.0016)/(k*.00076)=5.84795nC/m^2 (wrong by orders of magnitude)
3. C=epsilon*A/d=1(.00076)/.0016=47500000pF (orders of magnitude wrong)

(we seem to have been given a large amount of questions based on material that we didn't really cover very much if at all)

I feel like I should have the right answer based on the results of using these techniques in some of my other problems but seem to be wandering in the dark
Any help would be greatly appreciated
 
Last edited:
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εo is not equal to 1.
So check the C value.
Surface charge density = Q/A = C*V/A =(εo*A/d)*V/A
 

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