Calculating Electric Potential at Sphere and Shell

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SUMMARY

The discussion focuses on calculating the electric potential for a conducting sphere and a surrounding non-conducting spherical shell. The conducting sphere has a radius of 0.31 m and a charge of +4 µC, while the shell has a radius of 0.86 m and a charge of +1.5 µC. Key calculations include finding the electric potential at various points: 0.4 m outside the shell, at the shell's surface, midway between the sphere and shell, at the sphere's surface, and at the sphere's center. The calculations utilize the formula for electric potential derived from Gauss's Law, specifically applying the constant 9 x 10^9 N m²/C² for the electric potential due to point charges.

PREREQUISITES
  • Understanding of electric potential and Gauss's Law
  • Familiarity with spherical charge distributions
  • Knowledge of basic electrostatics concepts
  • Ability to perform calculations involving Coulomb's constant (9 x 10^9 N m²/C²)
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  • Study the application of Gauss's Law in electrostatics
  • Learn about electric potential due to spherical charge distributions
  • Explore the concept of electric fields in relation to charged conductors
  • Practice solving problems involving electric potential and charge distributions
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Students studying electrostatics, physics educators, and anyone seeking to understand electric potential calculations in spherical charge systems.

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Homework Statement



A conducting sphere with radius a = 0.31 m has a net charge Qa = +4 µC. A thin, non-conducting spherical shell of radius b = 0.86 m surrounds the sphere and is concentric with it. This shell has a net charge Qb = +1.5 µC distributed uniformly over its surface. The electric potential at infinity is zero.

(a) Calculate the electric potential at a radial distance of 0.4 m outside of the thin shell.
(b) Calculate the potential at the thin shell.
(c) Find the electric potential mid-way between the surface of the sphere and the surrounding shell.
(d) Find the potential at the surface of the sphere.
(e) Find the potential at the center of the sphere.

Homework Equations





The Attempt at a Solution



These are driving me crazy. My work gives me the following answers...
a) 9*10^9 (4*10^-6+1.5*10^-6/1.57)
b) 9*10^9(4*10^-6+1.5*10^-6/0.215)
c) 9*10^9(4*10^-6/0.585+1.5*10^-6/0.86)
d) 9*10^9(4*10^-6/0.31+1.5*10^-6/0.86)
e) 9*10^9(4*10^-6/0.31+1.5*10^-6)

which aren't right when I'm typing them in.
 
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