Spherical Capacitor with Charge, Potential Difference and More

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Homework Help Overview

The discussion revolves around a spherical capacitor problem involving charge, potential difference, and capacitance calculations. The original poster presents a scenario with specific values and seeks assistance in calculating capacitance and the radius of the inner sphere.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to calculate capacitance using the formula C = Q/V but encounters issues with the accepted answer format. Some participants suggest that significant digits or unit conversion may be factors. The poster also attempts to calculate the radius of the inner sphere using an incorrect formula for spherical capacitors, leading to confusion about the appropriate approach.

Discussion Status

Participants are actively engaging with the problem, offering suggestions regarding unit conversion and the need for a different formula for spherical capacitors. There is recognition of the original poster's mistakes, but no consensus on the correct method has been reached yet.

Contextual Notes

There is mention of specific homework requirements regarding units and significant figures, as well as the need for a different formula for spherical capacitors, which may not have been initially considered by the original poster.

Northbysouth
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Homework Statement


A spherical capacitor contains a charge of 3.10nC when connected to a potential difference of 220V . If its plates are separated by vacuum and the inner radius of the outer shell is 5.00cm .

Part A) Calculate the capacitance.

Homework Equations


C = Q/V

C = Aε0/d


The Attempt at a Solution



I tried plugging in the values into

C = Q/V

C = (3.1x10^-9 C)/220V
C = 1.409x10^-11 F

But it didn't accept this. Any suggestions?
 
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Maybe a matter of significant digits?
 
I made a mistake with the units. It wanted the answer in pico-Farads and I gave it in Farads. The answer is 14.1 pF.

Thanks for your help.
 
I'm stuck on the second part as well, it asks:

B) Calculate the Radius of the inner sphere

C = Aε0/d

where I believe that A is the area of a capacitor and d is the distance between them.

C = 4πr^3*ε0/d = 14.1

So I solved for r and I got

r = Cuberoot[(14.1x10^-12 F)*0.05 m/8.85x10^-12]

r = 0.2937 m = 29.37 cm

It says this is wrong and I don't know where to go from here.
 
Northbysouth said:
I'm stuck on the second part as well, it asks:

B) Calculate the Radius of the inner sphere

C = Aε0/d
This formula is valid for capacitors with plane, parallel plates.
For spherical capacitor there is a different formula.
You can look it up on Google if you don't have it.
 

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