A flat horizontal surface with an area of 650 cm2 is inside a uniform electric field of 2.99×104 N/C. The angle between the area vector and the electric field is 14.8°. What is the electric flux through the surface?
To find the electric flux through the surface, we can use the formula:
Electric flux (Φ) = Electric field (E) * Area (A) * cos(θ)
Where:
- Electric field (E) is given as 2.99×104 N/C
- Area (A) is given as 650 cm^2
- θ is given as 14.8°, but we'll need to convert it to radians before calculating the cosine.
First, let's convert the angle from degrees to radians:
θ (radians) = θ (degrees) * (π / 180)
θ (radians) = 14.8° * (π / 180)
θ (radians) = 0.2586 radians
Now we can substitute the given values into the formula:
Electric flux (Φ) = 2.99×104 N/C * 650 cm^2 * cos(0.2586 radians)
Note: We need to convert the area from cm^2 to m^2 to be consistent with the SI units of the electric field.
Since 1 cm^2 = (1/10,000) m^2:
Electric flux (Φ) = 2.99×104 N/C * (650/10,000) m^2 * cos(0.2586 radians)
Electric flux (Φ) ≈ 12.49 N·m^2/C (rounded to two decimal places)
Therefore, the electric flux through the surface is approximately 12.49 N·m^2/C.
To calculate the electric flux through the surface, we can use the formula:
Electric flux (Φ) = Electric field (E) * Surface area (A) * Cosine of the angle between the electric field and the normal to the surface (θ)
1. First, let's convert the surface area from cm^2 to m^2 since the electric field is given in N/C (SI units). There are 10,000 square centimeters in 1 square meter, so the surface area is 650 cm^2 * (1 m^2 / 10,000 cm^2) = 0.065 m^2.
2. Next, substitute the given values into the formula:
Electric flux (Φ) = (2.99×10^4 N/C) * (0.065 m^2) * cos(14.8°)
3. Calculate the cosine of the angle 14.8° using a scientific calculator: cos(14.8°) ≈ 0.970
4. Substitute the value of cos(14.8°) into the equation:
Electric flux (Φ) = (2.99×10^4 N/C) * (0.065 m^2) * 0.970
5. Finally, calculate the electric flux:
Electric flux (Φ) ≈ 120.471 N·m^2/C
Therefore, the electric flux through the surface is approximately 120.471 N·m^2/C.