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Find the capacitance of a spherical conductor of radius 9.0cm. Also find the charge required to give it a potential of 1000V.

Answer
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Hint: In order to find the value of the capacitance of a spherical conductor we use a direct formula for the capacitance and we take air as the dielectric material. Once the capacitance is calculated we can apply that value in the direct formula for the charge.

Complete step by step answer:
Let’s define all the terms which are given in the question
Radius of the spherical conductor, R=9.0cm=9×102m
Potential of the conductor, V=1000V
In the question, we are asked to find the value of the capacitance of a spherical conductor of radius 9.0cm and the charge required to give that conductor a potential of 1000V
First we are calculating the value of the capacitance of a spherical conductor
It is given that the conductor is spherical in shape and its radius is also given.
It is known that the capacitance of a spherical conductor is given by,
C=4πε0R………………. (1)
Where, C is the capacitance of a spherical conductor
ε0 is the permittivity of the dielectric material (Here, dielectric material is air)
(The permittivity of air, ε0=8.85×1012)
R is the radius of the conductor
Applying the known values in equation (1), we get,
C=4×3.14×8.85×1012×9×102
C=1000×1014F
C=10×1012F
C=10pF
That is, the value of the capacitance of a spherical conductor, C=10pF
Now we need to find the charge required to give that conductor a potential of 1000V
We know the charge of the charge of a conductor is given by the equation,
The charge of a conductor, Q=CV
Applying the known values to this equation, we get,
Q=10×1012×1000
Q=10×109C
That is, the charge required to give the spherical conductor of radius 9.0cm a potential of 1000V,
Q=10×109C.

Note: Capacitance is defined as the ratio of the amount of electric charge stored on a conductor to its difference in electric potential. There are two closely related notions of capacitance: mutual capacitance and self capacitance. SI unit of the capacitance is farad (F).