Cylindrical Capacitors Questions

Click For Summary
SUMMARY

The discussion focuses on the analysis of an isolated cylindrical capacitor consisting of two concentric conducting cylinders with radii a and b, and length L. The electric field between the conductors is determined to be E=Q/(2πε₀aL), while the electric potential difference is calculated as V=Q/(2πε₀a ln(b/a)). Consequently, the capacitance of the device is derived as C=ln(b/a)/(2πε₀a). The calculations are based on the equations for electric field, potential difference, and capacitance, confirming the correctness of the results presented.

PREREQUISITES
  • Understanding of electric fields and potential differences in cylindrical geometries
  • Familiarity with the equations for capacitance, specifically C=Q/V
  • Knowledge of integral calculus for evaluating electric potential
  • Proficiency in using the permittivity of free space, ε₀, in electrostatics
NEXT STEPS
  • Study the derivation of electric fields in cylindrical coordinates
  • Learn about the applications of Gauss's Law in electrostatics
  • Explore the concept of capacitance in different geometrical configurations
  • Investigate the effects of dielectric materials on capacitance
USEFUL FOR

This discussion is beneficial for physics students, electrical engineering students, and anyone studying electrostatics, particularly those focusing on capacitor design and analysis.

apphysicsgirl
Messages
9
Reaction score
0

Homework Statement


An isolated cylindrical capacitor consists of two concentric conducting cylinders of length L and radii a and b. The inner and outer conductors carry +Q and -Q, respectively.
a. Determine the electric field between the conductors.
b. Determine the electric potential difference between the two conductors.
c. What is the capacitance of this device?

Homework Equations


V=\intE dL
\ointE dA=Q/Epsilon
C=Q/V

The Attempt at a Solution


a. I got as my answer E=Q/(2\piEpsilon not (aL))
b. I used the integral with V and got Q/(2\piEpsilon not (a) (ln(b/a))
c. I plugged my answer from b into C=Q/V and got ln(b/a)/(2\piEpsilon not (a))


I am not sure if I did any of these right...
 
Physics news on Phys.org
apphysicsgirl said:

The Attempt at a Solution


a. I got as my answer E=Q/(2\piEpsilon not (aL))
b. I used the integral with V and got Q/(2\piEpsilon not (a) (ln(b/a))
c. I plugged my answer from b into C=Q/V and got ln(b/a)/(2\piEpsilon not (a))


I am not sure if I did any of these right...

Is the electric field independent of position?

ehild
 

Similar threads

Charge upon a parallel plate capacitor
  • · Replies 18 ·
Replies
18
Views
3K
Calculations involving different Dielectrics and Capacitors
  • · Replies 7 ·
Replies
7
Views
2K
Electric Field Inside Cylindrical Capacitor
  • · Replies 2 ·
Replies
2
Views
3K
Why Capacitors in Parallels vs. Series: Coaxial Capacitor Case
  • · Replies 2 ·
Replies
2
Views
2K
Maximum Voltage Between Long Coaxial Cylinders
  • · Replies 3 ·
Replies
3
Views
2K
Capacitor Problem with distance-dependent dieletric
  • · Replies 2 ·
Replies
2
Views
1K
Shell in a cylindrical capacitor
  • · Replies 1 ·
Replies
1
Views
2K
A disconnected capacitor with two dielectrics in parallel
  • · Replies 8 ·
Replies
8
Views
2K
How to find voltage across capacitor in RLC circuit?
  • · Replies 3 ·
Replies
3
Views
2K
Ranking charge stored on three capacitors by a battery
  • · Replies 6 ·
Replies
6
Views
3K