Question

An air capacitor has plate diameter 6cm. At what distance should the plates be placed so

as to have the capacitance of sphere of radius 90cm​

Answer 1

Given that,

Diameter = 6 cm

Radius of sphere= 90 cm

We need to calculate the area

Using formula of area

$A=\pi r^2$

Where, r = radius

Put the value into the formula

$A=\pi\times(3\times10^{-2})^2$

$A=0.00282\ m^2$

$A=2.82\times10^{-3}\ m^2$

We know that,

The capacitor of the plate is

$C=\dfrac{A\epsilon_{0}}{d}$....(I)

We need to calculate the distance between plates

Using formula of capacitance of sphere

$C=4\pi\epsilon_{0}R$

From equation (I)

$\dfrac{A\epsilon_{0}}{d}=4\pi\epsilon_{0}R$

$d=\dfrac{A}{4\pi\times R}$

Put the value into the formula

$d=\dfrac{2.82\times10^{-3}}{4\pi\times90\times10^{-2}}$

$d=0.00024\ m$

$d=2.4\times10^{-4}\ m$

Hence, The distance between plates is $2.4\times10^{-4}\ m$

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Topic : capacitance

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