Question

Variation in electric field for uniformly charged sphere is shown in figure then value of x :-

1) R/3
2) R/4
3) R/2
4) R/8​

Answer 1

Given:

Variation in electric field for uniformly charged sphere is shown.

To find:

Value of x ?

Calculation:

FROM THE GRAPH:

When r < R :

$\therefore \: E \propto \dfrac{r}{ {R}^{3}} \: \: . \: . \: . \: . \: (1)$

At r = x . . . . . .(x < R)

$\implies \: E \propto \dfrac{x}{ {R}^{3}}\: \: . \: . \: . \: . \: (2)$

When r > R : (using GAUSS'S LAW)

$\therefore \: E \propto \dfrac{1}{ {r}^{2} } \: \: . \: . \: . \: . \: (3)$

Comparing equations (2) and (3):

$\therefore \: \dfrac{x}{ {R}^{3} } = \dfrac{1}{ {r}^{2} }$

$\implies \: \dfrac{x}{ {R}^{3} } = \dfrac{1}{ {(2R)}^{2} }$

$\implies \: \dfrac{x}{ {R}^{3} } = \dfrac{1}{ 4{R}^{2} }$

$\implies \: x = \dfrac{R}{4}$

So, value of x = R/4.

• Please note that all the proportionalities can be proved by GAUSS' LAW. I have assumed that you know those derivations.

Answer 2

Answer:

R/4 is the correct answer to the question of yours