Electric Potential of Conducting Sphere: Charge & Charge Density

AI Thread Summary
To determine the charge and charge density on the surface of a conducting sphere with a radius of 0.21 m and a potential of 290 V, the relevant equations are v = kq/r and σ = q/SA, where SA is the surface area of the sphere. The initial calculation for charge (q) was incorrectly performed due to a mistake in applying the constant k, leading to an incorrect value of 5.5e11 C instead of the correct 6.8e-9 C. Consequently, the charge density calculation also yielded an incorrect result of 9.9e11 C/m² instead of the correct 1.2e-8 C/m². The error was identified as a miscalculation involving the constant k. Correct application of the equations is crucial for accurate results in electrostatics.
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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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