what is the capacitance of a sperical condoctor
Answers
Answer:
The capacitance for spherical conductors can be obtained by evaluating the voltage difference between the conductors for a given charge on each. It depends then on the inner and outer radius of each sphere.
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Explanation:
To calculate capacity of a spherical conductor, first calculate capacity for spherical shell:
onsider a spherical shell with inner radius a and out radius b. Now by applying Gauss' law to an charged conducting sphere, the electric field outside it is found to be :
E=
4πϵ
0
r
2
Q
The voltage between the spheres can be found by integrating the electric field along a radial line:
△V=
4πϵ
0
Q
∫
a
b
r
2
1
dr=
4πϵ
0
Q
[
a
1
−
b
1
]
From the defination of capacity :
C=
△V
Q
=
[
a
1
−
b
1
]
4πϵ
0
Now for sphere capacitor of radius R, a→R and b→∞
∴C=4πϵ
0
R
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