Question

a solid sphere of radius R is uniformly charged the ratio of magnitudes of electric field at distances r/2 and r from the centre is
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Answer 1

Given:

A solid sphere of radius R is uniformly charged.

To find:

The ratio of magnitudes of electric field at distances r/2 and r from the centre.

Calculation:

Let r < R ;

At a distance r/2 from centre:

$\therefore \: E1 = \dfrac{kqx}{ {R}^{3} }$

$= > \: E1 = \dfrac{kq( \frac{r}{2}) }{ {R}^{3} }$

$= > \: E1 = \dfrac{kqr }{ 2{R}^{3} }$

At a distance r from centre (i.e on the surface of the sphere):

$\therefore \: E2 = \dfrac{kq(r)}{ {R}^{3} }$

$= > \: E2 = \dfrac{kq r}{ {R}^{3} }$

So, required ratio is:

$= > \: E1 : E2= \dfrac{kqr}{ 2{R}^{3} } : \dfrac{kqr}{ {R}^{3} }$

$= > \: E1 : E2= 1 : 2$

So, final answer is:

$\boxed{ \sf{\: E1 : E2= 1 : 2}}$