Question

Draw the variation of electric field intensity of a shell of radius R with distance r .

Answer 1

To draw:

Variation of Electrostatic Field intensity of a shell with radius R and distance r having charge q.

Calculation:

At a distance r < R:

The shell doesn't enclose any charge;

$\therefore \displaystyle \: \int E.ds = \frac{q}{ \epsilon_{0}}$

$= > \displaystyle \: \int E.ds = 0$

$= > \: E= 0$

At a distance r = R :

The charge enclosed is q;

$\therefore \displaystyle \: \int E.ds = \frac{q}{ \epsilon_{0}}$

$= > E \times 4\pi {R }^{2} = \dfrac{q}{ \epsilon_{0}}$

$= > E = \dfrac{q}{ 4\pi\epsilon_{0} {R }^{2} }$

At a distance r > R:

The charge enclosed is q ;

$\therefore \displaystyle \: \int E.ds = \frac{q}{ \epsilon_{0}}$

$= > E \times 4\pi {r }^{2} = \dfrac{q}{ \epsilon_{0}}$

$= > E = \dfrac{q}{ 4\pi\epsilon_{0} {r }^{2} }$

Now, refer to the attached diagram.