Gauss law: Gauss’s law states that if a charge Q is enclosed by an arbitrary closed surface, then the total electric flux Φ through the closed surface is
A positive point charge Q is surrounded by an imaginary sphere of radius r as shown in figure. We can calculate the total electric flux through the closed surface of the sphere using the equation.
The electric field of the point charge is directed radially outward at all points on the surface of the sphere. Therefore, the direction of the area element d is along the electric field and θ = 0°
E is uniform on the surface of the sphere,
Substituting for
Q in equation 3, we get
The equation (4) is called as Gauss’s law. The remarkable point about this result is that the equation (4) is equally true for any arbitrary shaped surface which encloses the charge Q.
