Why Is Voltage Not Zero at Infinity in This Electrostatic Scenario?

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SUMMARY

The discussion centers on calculating the potential at a distance of r = 0.1 m from a point charge of -8 µC, surrounded by conducting spherical shells with specified radii. The potential at infinity is given as V(inf) = 1 x 10^5 V, which is crucial for determining the voltage difference from r = 0.9 m to infinity. The voltage difference is calculated by integrating the electric field from 0.9 m to infinity and adjusting for the specified potential at infinity, resulting in a total voltage of -509535 V at r = 0.1 m.

PREREQUISITES
  • Understanding of electrostatics and point charges
  • Familiarity with electric potential and voltage calculations
  • Knowledge of integration techniques in physics
  • Concept of conducting spherical shells and their effects on electric fields
NEXT STEPS
  • Study the principles of electric potential in electrostatics
  • Learn how to apply Gauss's Law for spherical charge distributions
  • Explore the integration of electric fields to find potential differences
  • Investigate the behavior of conductors in electrostatic equilibrium
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in advanced electrostatics, particularly in understanding potential differences in systems involving point charges and conducting shells.

jehan60188
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Homework Statement



A point charge q = -8 µC is surrounded by two thick, conducting spherical shells of inner and outer radii a1 = 0.2 m, a2 = 0.3 m, a3 = 0.8 m, and a4 = 0.9 m respectively. The inner shell is uncharged; the outer shell has a net charge Q = -8 µC. At this point in the problem, the potential at infinity is unspecified. Do not assume it is zero.


If now you are given V(inf) = 1 x 105 V, find the potential at r = 0.1 m.


Homework Equations



V = ∫E*dr

The Attempt at a Solution




voltage from .1 m to .9m = -359672 + -149863 = -509535
(known from previous steps)

I have no idea how to get the voltage from .9m to infinity!
 
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hi jehan60188! :smile:

the voltage difference from .9m to infinity is the same as it would be if the voltage at infinity was 0 :wink:
 
kk, since the voltage between point A (.9 m) and B (infinity) needs to be 10^5 higher than if it were supposed to be zero, I integrate from .9 to infinity, and then add 10^5
thanks!
 

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