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```Course:
Electric and Magnetic Fields(EMF)
Course Code:
PHY220
Textbooks: (1) Fundamental of Physics by HRK, 9thEdition/Chap.23
Lecture.24-27
Week.10(19-24Apr)
Instructor: Dr. Kaneez Rabia
1
Contents
Chapter.23
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Gauss´s Law
Flux
Flux of an electric field
Flux through a closed cylinder, uniform ﬁeld
Flux through a closed cube, nonuniform ﬁeld
Flux: Volume flow rate(volume per unit time) of any thing
Example: Air flow
(a) A uniform air
stream of velocity is
V perpendicular to
the plane of a square
loop of area A.
(b) The component of
V perpendicular to the
plane of the loop is
Vcos, where  is the
angle between V and a
normal to the plane.
(c) The area vector
A is perpendicular
to the plane of the
loop and makes an
angle  with V.
(d) The velocity
field intercepted
by the area of
the loop.
If V is parallel to the plane of the loop, no air moves through the loop, so  is zero. For
an intermediate angle , the rate  depends on the component of V normal to the
plane. Since that component is vcos, the rate of volume flow through the loop is
Fux of an electric ﬁeld
Flux through a closed cylinder, uniform ﬁeld
Flux through a closed cube, nonuniform ﬁeld
What is the electric flux through the right face,
the left face, and the top face?
Right face:
Left face:
• The differential area vector dA points
in the negative direction of the x axis,
and thus
• The term x again appears in our integration
and it is again constant over the face being
considered.
However, on the left face, x = 1.0 m. we ﬁnd
that the ﬂux through the left face is
Top face:
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