Question

Radius of spherical shell is 0.5 m. It is charged. Now imagine spherical surface of radius 2 m and 3 m concentric with spherical shell of 0.5 m radius. If electric field on these surfaces are E, and Es respectively, then​

Answer 1

Given:

Radius of spherical shell is 0.5 m. It is charged. Now imagine spherical surface of radius 2 m and 3 m concentric with spherical shell of 0.5 m radius.

To find:

Ratio of E and E_(s) ?

Calculation:

For a charged shell, when r > R :

$E = \dfrac{kq}{ {r}^{2} }$

$\implies E \: \propto \: \dfrac{1}{ {r}^{2} }$

So, the required ratio will be :

$\therefore \: \dfrac{E}{E_{s}} = \dfrac{{( r_{2})}^{2} }{{(r_{1})}^{2} }$

$\implies\: \dfrac{E}{E_{s}} = \dfrac{{(2)}^{2} }{{(3)}^{2} }$

$\implies\: \dfrac{E}{E_{s}} = \dfrac{4}{9}$

$\implies\: E : E_{s} = 4 : 9$

So, the required ratio is 4 : 9.