Spherical Capacitor with Charge, Potential Difference and More

[Northbysouth]

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?

 

[nasu]

Maybe a matter of significant digits?

 

[Northbysouth]

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.

 

[Northbysouth]

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.

 

[nasu]

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.