Electric Field Intensity due to a Uniformly Charged Non-conducting Sphere:
When charge is given to non-conducting sphere, it uniformly spreads throughout its volume. If q is the charge given and R is the radius of the sphere, then the volume charge density
(a) Outside the sphere : In this case taking O as centre and r as radius, a spherical Gaussian surface is drawn. The point P will be situated at this surface.
The direction of \(\vec E\) will be outwards directed due to symmetry. The charge enclosed by the Gaussian surface
Now equating equations (2) and (3), we get
In vector form
where \(\hat r\) = unit vector in direction OP.
(b) When point P is situated on the surface of the sphere : In this case we can consider the surface of the sphere as Gaussian surface. Therefore the whole charge of the sphere will again be charge enclosed. Thus by putting r = R in equation (5), we get
(c) When point P is inside the sphere (r < R):
Here also we draw a spherical Gaussian surface taking O as centre and r as radius. Point P will be situated at this surface. Now the charge enclosed by this Gaussian surface,
From the definition of the electric flux.
Again from equation (1)
(d) At the centre of the sphere: For central point
