Calculating Electric Flux

In summary: I would have to see the details of the calculation to have any chance of finding it.But, as I said, I agree with your calculation.
  • #1

Homework Statement


A 2cm x 3cm rectangle lies in the xy plane. What is the electric flux through the rectangle if
Electric field= (100i +50k) N/C

Homework Equations


Φe=E⋅Acosθ (Electric Flux Equation)

The Attempt at a Solution



My question is to find the magnitude of the electric field we say Emag=√(100i)2+(50k)2= 111.8N/C
Area=6x10-4m2
To find direction θ=tan-(50/100)=26.5°
We know that The angle in formula for electric flux is the angle subtended from a line normal to the surface and the electric field line. Therefore 90°-26.5°=63.4°
so:
Φe=E⋅Acosθ=(111.8N/C)(6x10-4m2)cos(63.4)=3.0x10-2

The textbook is disagreeing with this answer... Not sure what I am doing wrong.
 
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  • #2
The calculation is more straightforward if you consider that only the component that is perpendicular to the surface contributes to the flux. Nevertheless, your answer seems OK to me.
 
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  • #3
cookiemnstr510510 said:

Homework Statement


A 2cm x 3cm rectangle lies in the xy plane. What is the electric flux through the rectangle if
Electric field= (100i +50k) N/C

Homework Equations


Φe=E⋅Acosθ (Electric Flux Equation)

The Attempt at a Solution



My question is to find the magnitude of the electric field we say Emag=√(100i)2+(50k)2= 111.8N/C
Area=6x10-4m2
To find direction θ=tan-(50/100)=26.5°
We know that The angle in formula for electric flux is the angle subtended from a line normal to the surface and the electric field line. Therefore 90°-26.5°=63.4°
so:
Φe=E⋅Acosθ=(111.8N/C)(6x10-4m2)cos(63.4)=3.0x10-2

The textbook is disagreeing with this answer... Not sure what I am doing wrong.

What answer does the textbook give? By the way, for what it's worth, I agree with your numerical answer. A bit more below though about your method.

While I agree with the answer that you obtained, you made this way too complicated.

It's true that

[itex] \vec E \cdot \vec A = EA \cos \theta. [/itex]

But there is another way to express this relationship:

[itex] \vec E \cdot \vec A = E_x A_x + E_y A_y + E_z A_z, [/itex]

which is far more useful here.

You need to know both of these relationships. Sometimes one will be easier, and some other times the other will. You need to know both.
 
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  • #4
Ah
collinsmark said:
What answer does the textbook give? By the way, for what it's worth, I agree with your numerical answer. A bit more below though about your method.

While I agree with the answer that you obtained, you made this way too complicated.

It's true that

[itex] \vec E \cdot \vec A = EA \cos \theta. [/itex]

But there is another way to express this relationship:

[itex] \vec E \cdot \vec A = E_x A_x + E_y A_y + E_z A_z, [/itex]

which is far more useful here.

You need to know both of these relationships. Sometimes one will be easier, and some other times the other will. You need to know both.
Ahhh okay, makes it much easier. The book says 3.2x10^-5 Nm^2/C
 
  • #5
kuruman said:
The calculation is more straightforward if you consider that only the component that is perpendicular to the surface contributes to the flux. Nevertheless, your answer seems OK to me.
Thank you!
 
  • #6
cookiemnstr510510 said:
The book says 3.2x10^-5 Nm^2/C
Yeah, I suspect there is a mistake in your textbook, somewhere or another.
 

1. What is electric flux?

Electric flux is a measure of the electric field passing through a given area. It is represented by the symbol ΦE and is measured in units of volt-meters (V*m).

2. How is electric flux calculated?

Electric flux can be calculated by multiplying the electric field strength (E) by the area (A) that it passes through, and then taking the cosine of the angle between the field and the area. This can be represented by the equation ΦE = E * A * cosθ.

3. What is the unit of electric flux?

The unit of electric flux is volt-meters (V*m).

4. What is the difference between electric flux and electric field?

The electric field is a vector quantity that represents the force per unit charge at a given point in space. Electric flux, on the other hand, is a scalar quantity that measures the amount of electric field passing through a given area. In other words, electric field describes the strength of the electric force, while electric flux describes the amount of electric field passing through a given area.

5. Why is electric flux important?

Electric flux is an important concept in electromagnetism as it helps us understand the behavior of electric fields and their interactions with charges. It is also used in various engineering and scientific applications, such as in the design of electrical circuits and devices.

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