Download Document

PHY-AP -08 Electric Flux
By
Squadron Leader Zahid Mir
CS&IT Department , Superior University
Flux
• Flux is the property of every vector field.
• Flux means “ To Flow”. It is the measure
of the “flow” or penetration of the field
vectors through an imaginary fixed
surface in the field.
• Flux is the rate at which field lines passes
through the surface area.
Fluid Flow

When the area A is
perpendicular to the
flow velocity v, the
volume flow rate is
given as;
dV = vA
dt
Fluid Flow (Contd)

When the rectangle is tilted
at an angle so that its face
is not perpendicular to v,
the area that counts is the
shadow area that we see
when we look in the
direction of v.

The area that is outlined in
red and labeled A˩ in the
figure is the projection of
the area A onto a surface
perpendicular to v.
Fluid Flow (Contd)

Two sides of the projected rectangle
have the same length as the original
one, but the other two are foreshortened
by a factor cos ф , so the projected
area A˩ is equal to Acosф.
Electric Flux

Electric flux through the area held
perpendicular to the electric field
is the product of the field
magnitude E and area A.
фE = EA
 Increasing the area means more
lines of E pass through the area and
hence increase in flux.
 Stronger field means more closely
spaced lines of E and therefore more
lines per unit area, so again the flux
increases.
Electric Flux (Contd)

If the area is not perpendicular
to field E, then a fewer field
lines pass through it.

In this case the area that
counts is the silhouette area
(A˩)that we see when looking
in the direction of E.
Positive & Negative Flux

We can represent the direction of a vector area A by using the unit
vector perpendicular to the area;

A surface has two sides, so there are two possible directions of
and A.

If the direction of A is outward normal then the flux is known as
positive flux, and if the direction of A is normal inward then it is
negative.

Thus flux leaving the volume enclosed by the surface is
considered positive, and the flux entering the volume enclosed is
negative.
Flux through Irregular Surface in
a Non-Uniform Electric Field




Consider an arbitrary closed
surface immersed in a nonuniform electric field.
We divide the surface into small
squares each of area ∆A.
The direction of vector area ∆A
is taken as the outward drawn
normal to the surface.
The element area ∆A is so
small that E may be taken as
constant for all points on the
given square.

By summing the contributions of all the
elements, we obtain the total flux
through the surface.

The vectors
points in
different directions for the
various surface elements, but
at each point they are normal
to the surface and, by
convention, always point
outward.
 At the element labeled (1), the
field lines are crossing the
surface from the inside to the
outside and θ < 900; hence flux
through this element is positive.
 For element (2) the field lines
graze
the
surface
(perpendicular to the vector ∆Ai
); thus θ = 900 and the flux is
zero.
 For element (3), where the field
lines crossing the surface from
outside
to
inside,
0
0
180 > θ > 90 and the flux is
negative.

The net flux through the surface is proportional to
the net number of lines leaving the surface.
 Net number means the number leaving the surface minus
number entering the surface.
 If more lines are leaving than entering, then the net flux is
positive.
 If more lines are entering than leaving, the net flux is
negative.

This surface integral indicates that the surface is to
be divided into infinitesimal elements of area dA
and the scalar quantity E.dA is to be evaluated for
each element and summed over the entire surface.