Electric Potential of Conducting Sphere: Charge & Charge Density

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SUMMARY

The discussion focuses on calculating the charge and charge density of a conducting sphere with a radius of 0.21 m and a potential of 290 V. The correct charge (q) is determined using the formula q = Vr/k, yielding a value of 6.8E-9 C, while the charge density (σ) is calculated using σ = q/SA, resulting in 1.2e-8 C/m². The initial miscalculations were due to an error in applying the constant k, where the user mistakenly divided instead of multiplying.

PREREQUISITES
  • Understanding of electric potential and its relationship to charge
  • Familiarity with the formula for charge density (σ = q/SA)
  • Knowledge of the surface area of a sphere (SA = 4πr²)
  • Basic grasp of electrostatics, including Coulomb's law and constants like k
NEXT STEPS
  • Review the derivation and application of Coulomb's law in electrostatics
  • Study the concept of electric potential and its implications in different geometries
  • Learn about the properties of conductors in electrostatic equilibrium
  • Explore the implications of charge density in various physical contexts
USEFUL FOR

Students studying electrostatics, physics educators, and anyone interested in understanding the principles of charge distribution on conductors.

popo902
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Homework Statement



What are (a) the charge (in C) and (b) the charge density on the surface of a conducting sphere of radius 0.21 m whose potential is 290 V (with V = 0 at infinity)?

Homework Equations



v = kq/r
\sigma = q/SA
SA of a sphere = 4\pir^2

The Attempt at a Solution


so this is what i did
i used the first equation and solved for q = Vr/k
i plugged in the numbers
v= 290, r is the same as the radius because its only the surface r = 0.21,
k = 1/(4\pi\epsilon)
I got 5.5e11
the right answer is 6.8E-9

Then for the charge density,
i put the numbers in too
but this is also wrong for sure because it uses my q value
I got 9.9e11
the right answer is 1.2e-8

I don't know how i got that far off :frown:
 
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How did you get that value for q?

ehild
 
yeh sorry i realized i divided by 1/k istead of multiplying by k/1 :S
 

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