capacitance 2

2010-11-12 2:32 am

Suppose the charge on a metalsphere is Q. In order to find out C, we should useC=Q/V. but which point of the voltage do V refer to?

Now a neutral condoctor is brought near the metal sphere. what should the C change? If I use C=Q/V=4(pie)(permittivity)(r), all this variable should remain unchanged. Then it is correct the say the capacitance also remains unchanged?
I asked a question above, and here is the response from Mr.天同 ( 知識長) .

Q: Then it is correct the say the capacitance also remains unchanged?

Why do you think that the capacitance would change?. The capacitance of an object depends on its geometry and dimension, and doesn't depend on the charge stored on it.

This is similar to the capacity of a water tank depends only on its volume, and doesn't depend on the amount of water stored in it.

I think the answer is correct according to this expanation. But how can you explain if we use the eqution C=Q/V. Except form geometry and dimension, I think voltage can also affects the capacitance of the sphere. If this time a charged object insteal if neutral is placed near the meatl sphere, the voltage og the sphere definitely changes because of the electric field from the nearby object. Do you agree?

回答 (1)

Tom

2010-11-13 2:23 am

✔ 最佳答案

I guess you do not understand the proof of the capacitance of spherical capacitor?

You can assume there are two concentri spherical shells of radiii a and b. By using Gaussian surface wdrawing of radius r concentric with the two shells, q=(permittivity)EA=(permittivity)E(4(pi)r^2) where 4(pi)r^2 is the spherical surface area of the gassuian surface.

Therefore, we get E=1/[4(pi)(permittivity)] x q/r^2
V=Integrate(from a to b) Eds
= Integrate(from a to b)1/[4(pi)(permittivity)] x q/r^2
=q/[4(pi)(permittivity)](1/a-1/b)

Therefore, C=4(pi)(permittivity) ab/(b-a)

We can treat it as a single isolated spherical conductor of Radius R,and the another missing plate is from infinitely away.

So, a=R and b=infinitely long
C=4(pi)(permittivity) Rb/(b-R)
=4(pi)(permittivity) R/(1-R/b)
=4(pi)(permittivity) R

天同is right, the capacitance only depends on the geometry and dimension. If you use the equation q=CV, C is a constant for the same capacitor. Change in V will make change in q and via reverse.

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