الفيزياء العامة الجزء الثاني#موقع الفيزياء.كوم

4.2 The Electric Flux due to a point charge
To calculate the electric flux due to a point
charge we consider an imaginary closed
spherical surface with the point charge in the
center figure 4.5, this surface is called gaussian
surface. Then the flux is given by
Φ =
Φ =
Φ =
∫
E
r . dA
r
= E ∫ dAcosθ
(θ = 0)
q
πε r
2
4 ο
q
ε ο
∫ dA
=
q
4πε ο
r
2 4
πr
2
(4.3)
Lectures in General Physics
Note that the net flux through a spherical gaussian surface is proportional to
the charge q inside the surface.
Q
Figure 4.5
E
DdA
4.3 Gaussian surface
Consider several closed surfaces as shown in
figure 4.6 surrounding a charge Q as in the
figure below. The flux that passes through
surfaces S 1 , S 2 and S 3 all has a value q/ ε ο .
Therefore we conclude that the net flux through
any closed surface is independent of the shape of
the surface.
E
Q
S 1
S 2
S 3
Figure 4.6
E
Consider a point charge located outside a closed
surface as shown in figure 4.7. We can see that
the number of electric field lines entering the
surface equal the number leaving the surface.
Therefore the net electric flux in this case is
zero, because the surface surrounds no electric
charge.
Q
S
Figure 4.7
Dr. Hazem Falah Sakeek