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By the end of this section, you will be able to:
  • Define the concept of flux
  • Describe electric flux
  • Calculate electric flux for a given situation

The concept of flux    describes how much of something goes through a given area. More formally, it is the dot product of a vector field (in this chapter, the electric field) with an area. You may conceptualize the flux of an electric field as a measure of the number of electric field lines passing through an area ( [link] ). The larger the area, the more field lines go through it and, hence, the greater the flux; similarly, the stronger the electric field is (represented by a greater density of lines), the greater the flux. On the other hand, if the area rotated so that the plane is aligned with the field lines, none will pass through and there will be no flux.

Figure shows a shaded area in the center. Several arrows pointing right are shown behind, in front of and passing through the shaded area. These are labeled electric field.
The flux of an electric field through the shaded area captures information about the “number” of electric field lines passing through the area. The numerical value of the electric flux depends on the magnitudes of the electric field and the area, as well as the relative orientation of the area with respect to the direction of the electric field.

A macroscopic analogy that might help you imagine this is to put a hula hoop in a flowing river. As you change the angle of the hoop relative to the direction of the current, more or less of the flow will go through the hoop. Similarly, the amount of flow through the hoop depends on the strength of the current and the size of the hoop. Again, flux is a general concept; we can also use it to describe the amount of sunlight hitting a solar panel or the amount of energy a telescope receives from a distant star, for example.

To quantify this idea, [link] (a) shows a planar surface S 1 of area A 1 that is perpendicular to the uniform electric field E = E y ^ . If N field lines pass through S 1 , then we know from the definition of electric field lines ( Electric Charges and Fields ) that N / A 1 E , or N E A 1 .

The quantity E A 1 is the electric flux    through S 1 . We represent the electric flux through an open surface like S 1 by the symbol Φ . Electric flux is a scalar quantity and has an SI unit of newton-meters squared per coulomb ( N · m 2 /C ). Notice that N E A 1 may also be written as N Φ , demonstrating that electric flux is a measure of the number of field lines crossing a surface .

Figure a shows a rectangular shaded area in the xz plane. This is labeled S1. There are three arrows labeled E passing through S1. They are parallel to the y axis and point along the positive y axis.  Figure b, too has plane S1 and arrows E. Another plane, labeled S2 forms an angle theta with plane S1. Their line of intersection is parallel to the x axis. An arrow labeled n hat 2 forms an angle theta with E.
(a) A planar surface S 1 of area A 1 is perpendicular to the electric field E j ^ . N field lines cross surface S 1 . (b) A surface S 2 of area A 2 whose projection onto the xz -plane is S 1 .The same number of field lines cross each surface.

Now consider a planar surface that is not perpendicular to the field. How would we represent the electric flux? [link] (b) shows a surface S 2 of area A 2 that is inclined at an angle θ to the xz -plane and whose projection in that plane is S 1 (area A 1 ). The areas are related by A 2 cos θ = A 1 . Because the same number of field lines crosses both S 1 and S 2 , the fluxes through both surfaces must be the same. The flux through S 2 is therefore Φ = E A 1 = E A 2 cos θ . Designating n ^ 2 as a unit vector normal to S 2 (see [link] (b)), we obtain

Questions & Answers

A 40cm tall glass is filled with water to a depth of 30cm. A.what is the gauge pressure at the bottom of the glass? B.what is the absolute pressure at the bottom of the glass?
Abdulaziz Reply
A glass bottle full of mercury has mass 50g when heated through 35degree, 2.43g of mercury was expelled. Calculate the mass of the mercury remaining in the bottle
Anjorin Reply
Two electric point charges Q=2micro coulomb are fixed in space a distance 2.0cm apart. calculate the electric potential at the point p located a distance d/2 above the central point between two charges
Abdul Reply
what is wave
Ahmed Reply
What is charge bodies
Oje Reply
which have free elections
Usman
Show that if a vector is gradient of a scaler function then its line around a closed path is zero
Pak
Charge bodies are those which have free electons
Pak
the melting point of gold is 1064degree cencius and is boiling point is 2660 degree cenciu
Ilyas Reply
is Thomas's young experiment interference experiment or diffraction experiment or both
Ilyas Reply
An aqueous solution is prepared by diluting 3.30 mL acetone (d = 0.789 g/mL) with water to a final volume of 75.0 mL. The density of the solution is 0.993 g/mL. What is the molarity, molality and mole fraction of acetone in this solution?
eugene
A 4.0kg mess kit sliding on a fractionless surface explodes into two 2.0 kg parts.3.0 m/s due to north and 0.5 m/s 30 degree north of east. what is the speed of the mess kit
Shahid
it's a line used to represent a complex electrical quantity as a vector
Gift Reply
what is the meaning of phasor?
fitness Reply
The electric field inside a sphere of radius is given by the expression for some constants and. Find the charge density and the total charge contained in this sphere.
maloda Reply
what is motion?
Abdulaziz Reply
is the change of position of body
Kate
it's the process of moving something.
Gift
the state of a body in which it change its position with respect to sorrounding is known as motion for example player of football change its position with respect to spectator
Ilyas
it is a state of body in which it changes it,s position with respect to their time and immediate surrounding
Harish
a particle change with respect to time and position
Babak
it is a stat of body in which it changes its position with respect to mean and exstrem position
Manzoor
A 4.0 kg mass kit sliding on a fractionless surface explodes into two 2.0 kg parts,3.0 m/s due to north and 0.5 m/s 30 degree north of east. what the speed of mass kit
Shahid
momentum conservation
Mehmet
3.5 m/s north of east.
Mehmet
give me a compete solution
Shahid
where the solving of questions of this topic?
Bonifasi Reply
According to Nernst's distribution law there are about two solvents in which solutes undergo equilibria. But i don't understand how can you know which of two solvents goes bottom and one top? I real want to understand b'coz some books do say why they prefer one to top/bottom.
Elia Reply
I need chapter 25 last topic
Hafsa Reply
What is physics?
Abdulaziz
physics is the study of matter and energy in space and time and how they related to each other
Manzoor
interaction of matter and eneegy....
Abdullah
thanks for correcting me bro
Manzoor
What is electrostatics bassically?
Ehtisham Reply
study of charge at rest
wamis
A branch in physics that deals with statics electricity
Akona
what is PN junction?
Manzoor
Practice Key Terms 3

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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