Capaticance of thin spherical ball

In summary, the conversation discusses the existence of capacitance in a thin spherical ball with a charge placed near it. It is mentioned that there will be an induced charge on the shell of the ball, resulting in some capacitance. However, for a sphere, a reference point is needed to specify the capacitance, which can be taken as infinity to derive the capacitance of the ball. The conversation also mentions the potential on the surface of the ball and the potential at a reference point in infinity, which must be zero for finite energy.
  • #1
astro2cosmos
71
0
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?
 
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  • #2
yes there will be an induced charge on the shell due to which there will be some capacitance
 
  • #3
iitjee10 said:
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?
 
  • #4
Yes, you need a reference point to specify the capacitance of the spherical ball, due to

[tex]C = \frac{Q}{\phi(A) - \phi(B)}[/tex]

with [tex]\phi(A)[/tex]: potential on the surface of the ball; [tex]\phi(B)[/tex]: 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 [tex]B=\infty[/tex] (imagine a giant spherical capacitor which outer shell is in infinity with the potential [tex]\phi(\infty)=0[/tex]). In this term we can derive the capacitance of the spherical ball!
 
  • #5
saunderson said:
Yes, you need a reference point to specify the capacitance of the spherical ball, due to

[tex]C = \frac{Q}{\phi(A) - \phi(B)}[/tex]

with [tex]\phi(A)[/tex]: potential on the surface of the ball; [tex]\phi(B)[/tex]: 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 [tex]B=\infty[/tex] (imagine a giant spherical capacitor which outer shell is in infinity with the potential [tex]\phi(\infty)=0[/tex]). 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??
 
  • #6
astro2cosmos said:
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 [tex]R_2 \rightarrow \infty[/tex]... kind of hard to imagine, but if you don't have a reference point take it in infinity, cause there is always zero potential.
 

FAQ: Capaticance of thin spherical ball

What is capacitance?

Capacitance is a measure of an object's ability to store an electric charge. It is defined as the ratio of the electric charge on an object to the potential difference across the object.

How is capacitance calculated for a thin spherical ball?

The capacitance of a thin spherical ball can be calculated using the following formula: C = 4πεr, where C is the capacitance, ε is the permittivity of the material between the two conductors, and r is the radius of the sphere.

What factors affect the capacitance of a thin spherical ball?

The capacitance of a thin spherical ball is affected by the radius of the sphere, the distance between the two conductors, and the permittivity of the material between the conductors. It is also affected by the presence of any other nearby conductors or insulators.

How does the material of the thin spherical ball affect its capacitance?

The material of the thin spherical ball affects its capacitance through its permittivity, which is a measure of how easily electric fields can pass through the material. Materials with higher permittivity have a higher capacitance, while materials with lower permittivity have a lower capacitance.

What is the unit of measurement for capacitance?

The unit of measurement for capacitance is the farad (F). It is named after the scientist Michael Faraday and is defined as one coulomb of charge per volt of potential difference.

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