A uniform electric field of magnitude 3.00×10^4 N/C makes an angle of 37 degrees with a plane surface of area 1.40×10^−2 m^2.
What is the electric flux through this surface?
i got 321 using the formula
electricflux = E A Cos(theta), but it's wrong.
To calculate the electric flux through a surface, you need to use the formula:
Electric flux (Φ) = Electric field (E) * Area (A) * Cosine of the angle (θ)
Given:
Electric field (E) = 3.00 × 10^4 N/C
Area (A) = 1.40 × 10^(-2) m^2
Angle (θ) = 37 degrees
Let's plug in the values into the formula to find the electric flux:
Φ = (3.00 × 10^4 N/C) * (1.40 × 10^(-2) m^2) * cos(37 degrees)
Before calculating the cosine, make sure your calculator is set to degrees mode. Then evaluate the expression:
Φ ≈ (3.00 × 10^4 N/C) * (1.40 × 10^(-2) m^2) * cos(37 degrees)
≈ 1260 N·m^2/C
Therefore, the electric flux through the surface is approximately 1260 N·m^2/C.
To find the electric flux through the surface, you need to use the formula correctly. The formula you mentioned, electric flux = E * A * cos(theta), is indeed correct. However, it seems like there might be an error in your calculation.
Let's break down the calculation step by step:
1. Given that the magnitude of the electric field (E) is 3.00×10^4 N/C.
2. The area of the surface (A) is 1.40×10^−2 m^2.
3. The angle between the electric field and the surface (theta) is 37 degrees.
Now we can substitute these values into the formula:
Electric flux = E * A * cos(theta)
Electric flux = (3.00×10^4 N/C) * (1.4×10^−2 m^2) * cos(37 degrees)
To calculate the electric flux, make sure you use the angle in radians rather than degrees in the calculation. Let's convert 37 degrees to radians:
theta (in radians) = 37 degrees * (π/180)
theta (in radians) = 37 * (π/180)
theta (in radians) ≈ 0.6458 radians
Now substitute this value into the formula:
Electric flux = (3.00×10^4 N/C) * (1.4×10^−2 m^2) * cos(0.6458 radians)
Using a calculator, evaluate the cosine function:
Electric flux ≈ (3.00×10^4 N/C) * (1.4×10^−2 m^2) * 0.7933
Electric flux ≈ 3.3216 Nm^2/C
Therefore, the correct electric flux through the surface is approximately 3.3216 Nm^2/C.