A 30.0 cm diameter loop is rotated in a uniform electric field until the position of maximum electric flux is found. The flux in this position is 5.60 multiplied by 105 N·m2/C. What is the magnitude of the electric field?
MN/C
To find the magnitude of the electric field, we can use the formula for electric flux:
Electric flux (Φ) = E * A * cos(θ)
Where:
- Φ is the electric flux
- E is the electric field
- A is the area of the loop
- θ is the angle between the electric field and the normal to the loop's surface
In this case, we are given the diameter of the loop, which we can use to find the radius:
Radius (r) = Diameter / 2 = 30.0 cm / 2 = 15.0 cm = 0.15 m
The area of the loop can be calculated using the formula for the area of a circle:
Area (A) = π * r^2 = π * (0.15 m)^2
Now, we can rearrange the electric flux formula to solve for the electric field (E):
E = Φ / (A * cos(θ))
However, to find the angle between the electric field and the normal to the loop's surface (θ), we need more information. If we assume that the loop is perpendicular to the electric field, then θ = 0 degrees, and cos(θ) = 1.
Substituting the given values into the formula:
E = 5.60 x 10^5 N·m^2/C / (π * (0.15 m)^2)
E = 5.60 x 10^5 N·m^2/C / (3.1416 * (0.15 m)^2)
E = 5.60 x 10^5 N·m^2/C / (0.070685 m^2)
E ≈ 7.91 x 10^6 N/C
Therefore, the magnitude of the electric field is approximately 7.91 x 10^6 N/C.