Why Is My Electric Field Calculation for a Conducting Shell Incorrect?

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SUMMARY

The electric field calculation for a thin spherical conducting shell with a radius of 14.5 cm and a total charge of +39.1 micro coulombs was incorrectly computed due to a typographical error in the charge value. The correct formula for the electric field at a distance of 39.6 cm from the center is E = k * (q / r^2), where q should be 39.1 x 10^-6 C, not 3.91 x 10^-6 C. The expected result in megaNewtons per Coulomb (MN/C) is 2.24 MN/C, which was miscalculated due to this error.

PREREQUISITES
  • Understanding of electrostatics and electric fields
  • Familiarity with the formula E = k * (q / r^2)
  • Knowledge of charge distribution in conducting shells
  • Basic skills in unit conversion, particularly for megaNewtons per Coulomb
NEXT STEPS
  • Review the principles of electrostatics and Gauss's Law
  • Study the concept of electric fields around spherical charge distributions
  • Learn about unit conversions in electrostatics, specifically between Coulombs and megaNewtons
  • Practice calculating electric fields for various charge configurations
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Students in physics, electrical engineers, and anyone studying electrostatics who needs to understand electric field calculations for charged conductors.

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Consider a thin spherical shell of radius 14.5 cm with a total charge of +39.1 micro coulombs distributed uniformly on its surface. (Take radially outward as the positive direction.)
(b) Find the electric field 39.6 cm from the center of the charge distribution.

Round your answer to three significant figures.

...shouldn't the electric field at this point be given by E = k * (q / r ^ 2), where q is 3.91 x 10 ^ -6 C and r is 0.396 m? Same as a point charge right?
It wants the answer in megaNewtons / Coulomb; I give 2.24 MN/C and it's wrong? Why?

Thanks for any input.
 
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Your formula for the field is certainly correct since the charge is distributed uniformly on the shell and you're looking outside the shell. The only thing I can see is that in your post you say you used the value q = 3.91*10^-6 C when in fact 39.1 micro coulombs would be q = 39.1*10^-6 C. Maybe this is just a typo, or maybe that's your problem.
 

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