Gauss’s Law
Gauss’s law is defined as: Consider a point charge
Q at the center of a sphere of radius r which surrounds it completely. The
total numbers of tubes of flux originating from the charge is Q and are normal
to the surface of the sphere. The electric field E is normal to the surface and
all lines of force passing through the whole surface of the sphere.
However Gauss’s Law states that:
“The total electric flux through any
closed surface is proportional to the total electric charge inside the surface.”
The flux is independent and it only
depends on charge q enclosed by the sphere.
General form of Gauss’s law
Consider the surface is enclosed by the several charges
q1,q2,q3…….then the total electric field at any point is the sum of the
electric fields E of the individual charges.let q be the total charge enclosed
by the surface. Also consider
be
the total field at the position of the surface element. Then, we obtain
From this the General statement of Gauss’s Law is stated as
“The total electric flux through a closed surface is equal
to the total electric charge inside the surface, divided by εo.”
Applications of Gauss Law
This law is used for any distribution of charges and for any
closed surface to find the electric field of the sphere.