Electric Flux
Learning Objectives:
• Explain the principle of electric flux.
• Calculate the electric flux in a given surface area.
• Identify the applications of electric flux in
various electric fields.
Electric Flux
• Electric field lines always emerge from a positive
charge and end at a negative charge.
• The summation of these field lines is what is
termed as electric flux
Electric Flux
• “flux” is from the Latin word fluxus which
means flow.
• refers to the “rate of the flow of the electric
field” as determined by the number of electric
field or flux lines passing through a given region.
• Electric flux is the property of an electric field
relating to the measure of its strength.
Electric Flux
• Electric flux quantifies how many electric field
lines are going through an area.
▫ If the area is increased, we will get a greater flux
▫ If the electric field is increased, we will also get a
greater flux
Electric Flux
• Electric flux may be inward or outward, depending
on the direction of the electric field vectors.
Electric Flux
• A positive charge within a region will have an
outward electric flux passing through its
surface.
Electric Flux
• A negative charge will have an inward electric
flux through its surface.
Electric Flux
• A region containing a zero charge has “no net
electric flux” passing outward or inward.
Electric Flux
• In the case of uniform electric fields, the electric flux can
be calculated as
• The symbol for the flux is the capital Greek letter phi (𝚽),
while the subscript E indicates that we are calculating
electric flux. The SI unit for electric flux is Nm2 /C
• The “orientation of the surface relative to the lines of
force” greatly affects electric flux.
Electric Flux
1. When
A and
E are
parallel
When the electric field E
is parallel to the surface area
A, the angle between E and A
is equal to 0. Thus, the electric
flux is calculated as follows:
𝜱𝑬 = 𝑬 𝑨
Electric Flux
2. When A and E are at an angle
When the electric field E
passes through a tilted surface area A
at an orientation angle, then the flux
lines through this surface will be
proportional to this angle θ between
E and A. The electric flux can be
calculated as follows:
𝜱𝑬 = 𝑬 𝑨 𝒄𝒐𝒔𝜽
Electric Flux
3. When A and E are perpendicular
When the electric field E
and the surface area A are
perpendicular, the angle between
the area vector and the electric
field is 90°. Since cos90°=0,
there is no electric flux.
A uniform electric field with 9000 N/C is parallel to
a flat square area of 25 m2. Calculate the electric flux.
Given:
𝐸=
𝑁
9000 𝐶
𝐴 = 25 𝑚2
Required:
Calculate the electric flux (ΦE)
Solution:
Write the working equation
Φ𝐸 = 𝐸 𝐴
Substitute the given values.
Φ𝐸 = 9000 𝑁/𝐶 25𝑚2
𝑵𝒎𝟐
Φ𝑬 = 𝟐𝟐𝟓, 𝟎𝟎𝟎
𝑪
𝟐
𝑵𝒎
Φ𝑬 = 𝟐. 𝟐𝟓 × 𝟏𝟎𝟓
𝑪
Identify the electric flux passing through a rectangle with
sides of 13 m and 25 m found in a region with a uniform electric field
of 200 N/C and an angle of 55º with respect to the horizontal.
Given:
𝑙 = 25 𝑚
𝑤 = 13 𝑚
𝐸 = 200 𝑁/𝐶
𝜃 = 55°
Required:
Calculate the electric flux (ΦE)
Given:
𝑙 = 25 𝑚
𝐸 = 200 𝑁/𝐶
𝑤 = 13 𝑚
𝜃 = 55°
Solution:
Solve for the area (A)
𝐴=𝑙 𝑤
𝐴 = 25 𝑚 13𝑚
𝑨 = 𝟑𝟐𝟓𝒎𝟐
Substitute the given values
Φ𝐸 = 𝐸 𝐴 𝑐𝑜𝑠𝜃
Φ𝐸 = 200 𝑁/𝐶 325𝑚2 cos 55°
𝑵𝒎𝟐
Φ𝑬 = 𝟑𝟕, 𝟐𝟖𝟐. 𝟒𝟕
𝑪
𝟐
𝑵𝒎
Φ𝑬 = 𝟑. 𝟕𝟑 × 𝟏𝟎𝟒
𝑪
Electric Flux