How Do You Calculate the Potential Difference Between Coaxial Conductors?

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SUMMARY

The discussion focuses on calculating the potential difference between coaxial conductors with diameters of 0.002m for the inner conductor and 0.016m for the outer conductor, both carrying line charge densities of +/- 5.6 x 10^-10 C/m. The electric field (E) is defined using the formula E = L/(2πε₀r), where L is the linear charge density and ε₀ is the permittivity constant. The potential difference is derived from the electric field using the equation V = -∫E dl, leading to the expression V = (L/(2πε₀)) ln(rb/ra), where rb and ra are the outer and inner radii, respectively. The challenge arises from the presence of charge on both conductors, complicating the calculation of the potential difference.

PREREQUISITES
  • Understanding of electric fields in cylindrical charge distributions
  • Familiarity with the concept of linear charge density
  • Knowledge of integration in the context of electric potential
  • Basic grasp of permittivity constant (ε₀) in electrostatics
NEXT STEPS
  • Study the derivation of electric fields for cylindrical conductors
  • Learn about the application of Gauss's Law in electrostatics
  • Explore the concept of electric potential and its calculation methods
  • Investigate the effects of multiple charge distributions on potential difference
USEFUL FOR

Students and professionals in physics, electrical engineering, and anyone involved in electrostatics or studying electric fields and potentials in coaxial systems.

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Homework Statement



A co-axial consists of .002m diameter inner conductor and an outer conductor of .016m diameter (thickness is negligible). If the conductors carry line charge densities of +/- 5.6*10^-10 C/m, what is the magnitude of the potential difference between them.


Homework Equations



I know that the electric field for any continuous cylindrically symmetric charge distribution with linear charge density L

E= L/(2*pi*constant*r)

-----

I know that the electric field at the surface of any conductor is (Surface charge density)/constant.

I Know that Potential= -SE* dl

S is integral sign.


Constant is the permutivity constant, I don't know how to put the symbol on here.


The Attempt at a Solution



Well I know that the magnitude of the electric potential outside of any line of charge

E= L/(2*pi*constant) times ln(rb/ra) where rb is radius outside line and ra is the radius of the distribution. Its the fact that the outside radius in this case is also charge which is throwing me off
 
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It may help you that inside long cylinder with homogeneous charge density E=0.
 

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