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Q. The electric field due to a uniformly charged sphere of radius $R$ as a function of the distance from its centre is represented graphically by

AIIMSAIIMS 2004Electric Charges and Fields

Solution:

Outside the spherical charge, the intensity of electric field at a point $P$ situated at a distance $r$ from the centre of the charge is
image
$E=\frac{1}{4 \pi \varepsilon_{0}} \frac{q}{r^{2}} (\text { if } r>R) $
On the surface of spherical charge the electric field is given by
$E=\frac{1}{4 \pi \varepsilon_{0}} \frac{q}{r^{2}}$ (if $ r=R )$
and inside the spherical charge the electric field is
$E=\frac{1}{4 \pi \varepsilon_{0}} \frac{q r}{R^{3}} $ (if $ r < R)$
Hence, the variation of $E-r$ is a follows :
image