Question

Find the equation
of
capacitance
spherical conductor


shown below and
using
the equation
deduce
the
value of capacitance
of
earth (take radius of earth
as 6400 km)
+​

Answer 1

Answer:

HHHHHHHHHHHH hahahah happy birthday

Answer 2

To derive:

Expression for capacitance of a spherical capacitor.

Derivation:

For a spherical capacitor of radius "r", we can say that its surface potential will be :

$\therefore \: V = \dfrac{1}{4\pi \epsilon_{0}} \bigg(\dfrac{q}{r} \bigg)$

So, let capacitance be C ;

$\therefore \: C = \dfrac{q}{V}$

$= > \: C= \dfrac{q}{\dfrac{1}{4\pi \epsilon_{0}} \bigg(\dfrac{q}{r} \bigg)}$

$= > \: C= \dfrac{1}{\dfrac{1}{4\pi \epsilon_{0}} \bigg(\dfrac{1}{r} \bigg)}$

$= > \: C= 4\pi \epsilon_{0} r$

So, expression for capacitance is :

$\boxed{ \bold{ \large{\: C= 4\pi \epsilon_{0} r}}}$

Now , for earth , radius is 6400 km , putting the available values in SI units:

$= > \: C= 4\pi \epsilon_{0} \times (6400 \times {10}^{3} )$

$= > \: C= \dfrac{1}{9 \times {10}^{9} } \times (6400 \times {10}^{3} )$

$= > \: C= \dfrac{1}{9 \times {10}^{6} } \times (6400 )$

$= > \: C= \dfrac{711.11}{ {10}^{6} }$

$= > \: C= 711.11 \times {10}^{ - 6} \: H$

$\boxed{ \bold{ = > \: C= 711.11 \: \mu H }}$

HOPE IT HELPS.