How to Calculate Electric Flux Through a Tilted Box?

[zooboodoo]

Homework Statement

A empty cardboard box is placed in an electric field pointing upwards with a strength of 1100 N/C as shown above. The bottom of the box is tilted up by an angle Θ = 19° from the horizontal. Side A of the box faces out of the page and is 10 cm high and 14 cm long. Sides B and C are 10 cm high and 12 cm deep. Sides D and E are 14 cm long and 12 cm deep.

calculate flux through each side of the box

Homework Equations

I have the equation Flux=EAcostheta

The Attempt at a Solution

(1100)(120)(cos71) did not give me the right answer, so I thought I would try cos19, but that also didn't work. ( that is for side B) I'm not sure if I'm missing something conceptually, I also tried the negatives for both of these answers, the flux is flowing through the side, to my understanding, i don't see when the flux would NOT be going through the side in order to get a negative result. If someone could help me grasp where I'm going wrong with one of the sides i would greatly appreciate it.

 

[tiny-tim]

Hi zooboodoo!

which is the base of the box? which edge is still on the table?

 

[thomate1]

I would first like to clarify the concept of electric flux. Electric flux is a measure of the electric field passing through a given area. It is defined as the product of the electric field strength and the area perpendicular to the field. In this case, the electric flux through each side of the box can be calculated using the formula: Flux = E * A * cosθ, where E is the electric field strength, A is the area of the side, and θ is the angle between the electric field and the area vector.

Now, let's consider the calculation of flux through side B of the box. The correct equation to use would be Flux = E * A * cosθ, where E is the electric field strength of 1100 N/C, A is the area of side B (12 cm * 10 cm = 120 cm^2), and θ is the angle between the electric field and the area vector. Since the electric field is pointing upwards and side B is tilted at an angle of 19° from the horizontal, the angle between the field and the area vector is 90° - 19° = 71°. Therefore, the correct calculation would be Flux = (1100 N/C) * (120 cm^2) * cos(71°) = 1100 * 120 * 0.342 = 44880 N·cm^2.

It is important to note that the angle used in the cosθ term should always be the angle between the electric field and the area vector. In this case, the angle between the electric field and the area vector for side B is 71°, not 19°.

I would also like to mention that the negative sign in the equation is used to indicate the direction of the electric flux. In this case, since the electric field is pointing upwards and side B is facing out of the page, the electric flux through side B is positive. However, if the electric field was pointing downwards and side B was facing into the page, the electric flux would be negative.

I hope this explanation helps you understand the concept of electric flux and how to correctly calculate it through each side of the box. If you have any further questions, please feel free to ask.