To determine the electric flux through a surface in a uniform electric field, we can use the formula for electric flux (\( \Phi_E \)): \[ \Phi_E = E \cdot A \cdot \cos(\theta) \] Where: - \( \Phi_E \) is the electric flux (in Nm²/C), - \( E \) is the electric field strength (in N/C), - \( A \) is the area of the surface (in m²), - \( \theta \) is the angle between the electric field lines and the normal (perpendicular) to the surface. ### Step-by-Step Explanation: 1. **Identify the Given Values**: - Electric field strength, \( E = 5 \, \text{N/C} \) - Area of the surface, \( A = 2 \, \text{m}^2 \) - Since the surface is oriented perpendicular to the electric field lines, the angle \( \theta = 0^\circ \). 2. **Calculate the Cosine of the Angle**: - The cosine of \( 0^\circ \) is \( 1 \): \[ \cos(0^\circ) = 1 \] 3. **Substitute the Values into the Formula**: - Now we can substitute the values into the electric flux formula: \[ \Phi_E = E \cdot A \cdot \cos(\theta) = 5 \, \text{N/C} \cdot 2 \, \text{m}^2 \cdot 1 \] 4. **Perform the Calculation**: - Multiply the values: \[ \Phi_E = 5 \cdot 2 \cdot 1 = 10 \, \text{Nm}^2/\text{C} \] ### Conclusion: The electric flux through the surface is \( 10 \, \text{Nm}^2/\text{C} \). Therefore, the correct option is **C**. ### Explanation of Other Options: - **Option A: 0 Nm²/C**: This option would be correct if the surface were oriented parallel to the electric field lines (i.e., \( \theta = 90^\circ \)), where \( \cos(90^\circ) = 0 \). However, since the surface is perpendicular to the field lines, this option is incorrect. - **Option B: 5 Nm²/C**: This value would be obtained if the area were 1 m² (since \( 5 \, \text{N/C} \cdot 1 \, \text{m}^2 = 5 \, \text{Nm}^2/\text{C} \)). However, with an area of 2 m², this option does not apply. - **Option D: 25 Nm²/C**: This option would imply an electric field strength of 12.5 N/C with an area of 2 m² (since \( 12.5 \, \text{N/C} \cdot 2 \, \text{m}^2 = 25 \, \text{Nm}^2/\text{C} \)). This is not the case here, as the electric field strength is only 5 N/C. ### Revision Summary: - Electric flux (\( \Phi_E \)) is calculated using \( \Phi_E = E \cdot A \cdot \cos(\theta) \). - For a surface perpendicular to the electric field, \( \theta = 0^\circ \) and \( \cos(0^\circ) = 1 \). - The electric flux through the surface is \( 10 \, \text{Nm}^2/\text{C} \) when \( E = 5 \, \text{N/C} \) and \( A = 2 \, \text{m}^2 \). - Always check the orientation of the surface relative to the electric field to determine the correct angle for calculations.