To find the electric flux through a surface, we can use the formula for electric flux, which is defined as the product of the electric field and the area of the surface, adjusted for the angle between the electric field and the area vector. The formula is given by:
Electric Flux Formula
The electric flux (Φ) can be expressed mathematically as:
Φ = E × A × cos(θ)
Where:
- Φ = electric flux
- E = magnitude of the electric field
- A = area of the surface
- θ = angle between the electric field and the area vector
Given Values
In your case, the values provided are:
- Electric field (E) = 3 N/C
- Area (A) = 3.55 m²
- Angle (θ) = 90°
Calculating the Electric Flux
Since the angle θ is 90°, we can substitute this into the formula. The cosine of 90 degrees is 0:
cos(90°) = 0
Now, substituting the values into the electric flux formula:
Φ = E × A × cos(θ)
Φ = 3 N/C × 3.55 m² × cos(90°)
Φ = 3 N/C × 3.55 m² × 0
Φ = 0
Understanding the Result
The result of the electric flux being zero makes sense in this context. When the area vector is perpendicular to the electric field (which is what happens when θ is 90°), no electric field lines pass through the surface. Therefore, the electric flux through that surface is zero.
This concept is crucial in understanding how electric fields interact with surfaces. It illustrates that the orientation of the surface relative to the electric field significantly affects the amount of electric flux that can pass through it. In practical terms, if you were to visualize this, imagine a flat surface facing directly away from the direction of the electric field lines; no lines would intersect the surface, leading to zero flux.
