Equipotential surfaces; finding the radius

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SUMMARY

The discussion focuses on calculating the radius of equipotential surfaces for a charged metal sphere with a radius of 0.39 m and a charge of 0.55 μC. The formula used is V = kQ / r, where k is the Coulomb's constant (9.0 x 10^9 Nm²/C²). The user attempts to find the radii for the first, tenth, and hundredth equipotential surfaces, which are spaced 100 V apart. The solution requires determining the potential of the sphere itself before calculating the radii of the equipotential surfaces.

PREREQUISITES
  • Understanding of electrostatics and electric potential
  • Familiarity with the formula V = kQ / r
  • Knowledge of equipotential surfaces and their properties
  • Basic algebra for solving equations
NEXT STEPS
  • Calculate the potential of the sphere using V = kQ / r
  • Determine the radius for the first equipotential surface at 100 V
  • Extend calculations to find the radii for the tenth and hundredth equipotential surfaces
  • Explore the concept of equipotential surfaces in three-dimensional space
USEFUL FOR

Students studying electrostatics, physics educators, and anyone interested in understanding electric potential and equipotential surfaces in electrostatics.

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Homework Statement



a metal sphere of radius 0.39 m carries a charge 0.55 μC. Equipotential surfaces are to be drawn for 100-V intervals outside of the sphere.

Determine the radius of the first, tenth and 100th equipotential from the surface.


Homework Equations



V = kQ / r
Volt = (Coulombs Constant * Charge) / radius

The Attempt at a Solution



r = ((9.0X10^9 Nm²/C²)(.55X10^-6 C))/ (1 Nm/C)

r = ((9.0X10^9 Nm²/C²)(.55X10^-6 C))/ (10 Nm/C)

r = ((9.0X10^9 Nm²/C²)(.55X10^-6 C))/ (100 Nm/C)

all units cancel out and I'm left with meters but I'm getting the incorrect values according to the homework system that I'm using
 
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Read the problem more carefully. The equipotential surfaces are 100 V apart.

What is the potential of the sphere itself? Start there.
 

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