Capaticance of thin spherical ball

[astro2cosmos]

suppose there is a uncharged thin spherical ball (thickness tends to 0) then Does if have any capacitance if a +q charge is placed near it?

 

[iitjee10]

yes there will be an induced charge on the shell due to which there will be some capacitance

 

[astro2cosmos]

yes there will be an induced charge on the shell due to which there will be some capacitance

ok! but capacitance is always b/w two quantities having a distance d.then for a sphere?

 

[saunderson]

Yes, you need a reference point to specify the capacitance of the spherical ball, due to

$$C = \frac{Q}{\phi(A) - \phi(B)}$$

with $$\phi(A)$$: potential on the surface of the ball; $$\phi(B)$$: potential on the surface, the reference point is on

If the reference point is in infinity, we know that the potential in infinity must vanish, cause only in this case the energy is finite. So we can take $$B=\infty$$ (imagine a giant spherical capacitor which outer shell is in infinity with the potential $$\phi(\infty)=0$$). In this term we can derive the capacitance of the spherical ball!

 

[astro2cosmos]

Yes, you need a reference point to specify the capacitance of the spherical ball, due to

$$C = \frac{Q}{\phi(A) - \phi(B)}$$

with $$\phi(A)$$: potential on the surface of the ball; $$\phi(B)$$: potential on the surface, the reference point is on

If the reference point is in infinity, we know that the potential in infinity must vanish, cause only in this case the energy is finite. So we can take $$B=\infty$$ (imagine a giant spherical capacitor which outer shell is in infinity with the potential $$\phi(\infty)=0$$). In this term we can derive the capacitance of the spherical ball!

i didn't get the phi(B)}[/tex]. which surface do you mention here??

 

[saunderson]

i didn't get the phi(B)}[/tex]. which surface do you mention here??

This surface is in infinity ! Like I've said, imagine a giant spherical capacitor, with the inner shell of radius R1="radius of your spherical ball" and the the outer shell $$R_2 \rightarrow \infty$$... kind of hard to imagine, but if you don't have a reference point take it in infinity, cause there is always zero potential.