Q. Which of the following plots represents the variation of the electric field with distance from the centre of a uniformly charged non-conducting sphere of radius $R$ ?
Rajasthan PMTRajasthan PMT 2006Electric Charges and Fields
Solution:
The electric field intensity at a point lying outside the sphere (non-conducting) is
$E = \frac{ 1}{ 4 \pi \varepsilon_0} \frac{ q}{ r^2 } $
where $r$ is the distance of that point from centre of sphere.
$\therefore E \propto \frac{ 1}{r^2} $ ..( i)
The electric fieid intensity at surface of sphere
$E = \frac{ q}{ 4 \pi \varepsilon_0 R^2}$
or $E \propto \frac{ 1}{R^2} $ ..( ii)
$R$, being the radius of sphere.
The eiectric field intensity at a point Iying inside the sphere is
$E = \frac{ qr}{ 4 \pi \varepsilon_0 R^3}$
or $E \propto r $ ..( iii)
Also at the centre of sphere $r = 0$.
Hence, $E = 0$. The graphical distribution is shown below
