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?
Bihar CECEBihar CECE 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.
$\therefore E \propto \frac{1}{r^{2}} \ldots$(i)
The electric field intensity at surface of sphere
$ E=\frac{q}{4 \pi \varepsilon_{0} R^{2}}$
or $E \propto \frac{1}{R^{2}} \ldots$(ii)
$R$, being the radius of sphere. The electric field intensity at a point lying inside the sphere is
$E=\frac{q r}{4 \pi \varepsilon_{0} R^{3}}$
or $E \propto r \ldots$(iii)
Also at the centre of sphere $r=0 .$
Hence, $E=0$.
The graphical distribution is shown below:
