Final answer:
To find the electric flux through a circular area in a uniform electric field, one can calculate the area of the circle and multiply it by the magnitude of the electric field. The electric flux is equal to the product of the electric field, the area of the circle, and the cosine of the angle between them, which is zero in this case.
Step-by-step explanation:
The question inquires about the electric flux through a circular area with a given radius, situated in a uniform electric field. To calculate the electric flux (Φ), we use the formula Φ = E × A × cos(θ), where E is the electric field strength, A is the area through which the field lines pass, and θ is the angle between the field lines and the normal to the surface.
In this scenario, since the field is uniform and the circular area lies in the xy-plane, θ is 0 degrees because the electric field lines are perpendicular to the area. We calculate the area (A) of the circle using the formula A = πr², where r is the radius of the circle. Thus, A = π × (2.2 m)².
Therefore, with an electric field magnitude of 1 N/C and r = 2.2 m, the electric flux can be found as follows:
- A = π × (2.2 m)² = 15.2052 m² (approximately)
- Φ = E × A × cos(0°) = 1 N/C × 15.2052 m² × 1
- Φ = 15.2052 N·m²/C (approximately)
The electric flux through the circular area is therefore approximately 15.2052 N·m²/C.