A closed surface is constructed in the space between two large parallel metal plates, where there is a constant electric field E. The magnitude of the field is |E| = 1880 N/C. The numbers (1), (2), and (3) in the simulation label small increments of area of 1.1 cm^2 on the surface. The direction of each increment is defined to be the direction of a vector out of the surface and perpendicular to the increment's surface area. With that definition assume the direction of the first increment ΔA1 is 65° from the direction of E, that the second increment ΔA2 is oriented 90° from the direction of E, and that the third increment ΔA3 is oriented 135° from the direction of E. Find the flux through each of the three increments of area
I use the formula Phi=EAcos(θ)
For ΔA1 I got 1880(.00011m^2)cos(65)=.05486N*m^2/C but this is not the answer. Can somebody show how to get to the answer key .0874N*m^2/C? Once I know how I will do the rest for the 2 and 3
To find the flux through each of the three increments of area, we can use the formula:
Φ = E * A * cosθ
where Φ is the flux, E is the electric field, A is the area vector, and θ is the angle between the electric field and the area vector.
Let's calculate the flux through each increment of area:
1. For increment ΔA1:
Angle θ = 65°
Area A = 1.1 cm^2 = 0.011 m^2
Flux Φ1 = |E| * A * cosθ
Substituting the given values:
Flux Φ1 = 1880 N/C * 0.011 m^2 * cos(65°)
2. For increment ΔA2:
Angle θ = 90°
Area A = 1.1 cm^2 = 0.011 m^2
Flux Φ2 = |E| * A * cosθ
Substituting the given values:
Flux Φ2 = 1880 N/C * 0.011 m^2 * cos(90°)
3. For increment ΔA3:
Angle θ = 135°
Area A = 1.1 cm^2 = 0.011 m^2
Flux Φ3 = |E| * A * cosθ
Substituting the given values:
Flux Φ3 = 1880 N/C * 0.011 m^2 * cos(135°)
Now, you can compute the values for Φ1, Φ2, and Φ3 using the above formulas.
To find the flux through each of the three increments of area, we need to use the equation for electric flux, which is given by:
Φ = E * A * cos(θ)
where:
- Φ is the electric flux
- E is the magnitude of the electric field
- A is the area vector
- θ is the angle between the electric field and the area vector
Let's calculate the flux through each increment step by step:
1. For increment ΔA1:
- Magnitude of the electric field, |E| = 1880 N/C
- Area, A = 1.1 cm^2 = 1.1 * 10^-4 m^2
- Angle between the electric field and the area vector, θ = 65°
Substituting these values into the formula, we have:
Φ1 = |E| * A * cos(θ)
Φ1 = 1880 N/C * 1.1 * 10^-4 m^2 * cos(65°)
2. For increment ΔA2:
- Magnitude of the electric field, |E| = 1880 N/C
- Area, A = 1.1 cm^2 = 1.1 * 10^-4 m^2
- Angle between the electric field and the area vector, θ = 90°
Substituting these values into the formula, we have:
Φ2 = |E| * A * cos(θ)
Φ2 = 1880 N/C * 1.1 * 10^-4 m^2 * cos(90°)
3. For increment ΔA3:
- Magnitude of the electric field, |E| = 1880 N/C
- Area, A = 1.1 cm^2 = 1.1 * 10^-4 m^2
- Angle between the electric field and the area vector, θ = 135°
Substituting these values into the formula, we have:
Φ3 = |E| * A * cos(θ)
Φ3 = 1880 N/C * 1.1 * 10^-4 m^2 * cos(135°)
Now, you can calculate the numerical values for each increment using a scientific calculator or trigonometric tables.
angle wrong, 65 to normal is 25 to surface. zero would be flat against your hot plate 90 - 65 = 25
1880(.00011m^2)cos(25) = 0.1874 not 0.0874