To determine the electric flux through a surface of area \( A \) placed perpendicular to a uniform electric field \( E \), we need to understand the concept of electric flux and how it is calculated. ### Correct Option: **B. \( E \times A \)** ### Detailed Explanation: 1. **Understanding Electric Flux**: - Electric flux (\( \Phi_E \)) is a measure of the electric field passing through a given area. It quantifies how much electric field lines penetrate a surface. - The formula for electric flux is given by: \[ \Phi_E = E \cdot A \cdot \cos(\theta) \] where: - \( \Phi_E \) is the electric flux, - \( E \) is the magnitude of the electric field, - \( A \) is the area of the surface, - \( \theta \) is the angle between the electric field lines and the normal (perpendicular) to the surface. 2. **Surface Orientation**: - In this case, the surface is placed **perpendicular** to the electric field. This means that the angle \( \theta \) is \( 0^\circ \). - The cosine of \( 0^\circ \) is 1, so the formula simplifies to: \[ \Phi_E = E \cdot A \cdot \cos(0^\circ) = E \cdot A \cdot 1 = E \cdot A \] 3. **Conclusion**: - Therefore, the electric flux through the surface is simply the product of the electric field strength and the area of the surface when the surface is perpendicular to the field. ### Why Other Options Are Incorrect: - **Option A: [blank]** - This option is not defined, so it cannot be correct. - **Option C: [blank]** - Similar to Option A, this option is not defined, so it cannot be correct. - **Option D: \( \frac{E}{A} \)** - This option is incorrect because it suggests that electric flux is inversely proportional to the area, which is not true. Electric flux increases with an increase in area when the electric field is constant. The correct relationship is directly proportional, as shown in the correct option \( E \times A \). ### Common Pitfalls: - **Misunderstanding the Angle**: Students often forget to consider the angle between the electric field and the surface normal. If the surface is not perpendicular, the angle must be taken into account. - **Confusing Flux with Field Strength**: Electric flux is not the same as electric field strength. Flux is a measure of the total field passing through an area, while field strength is a measure of force per unit charge. ### Revision Summary: - Electric flux (\( \Phi_E \)) is calculated using the formula \( \Phi_E = E \cdot A \cdot \cos(\theta) \). - For a surface perpendicular to the electric field, \( \theta = 0^\circ \), leading to \( \Phi_E = E \cdot A \). - The correct answer for the electric flux through a surface of area \( A \) in a uniform electric field \( E \) is \( E \times A \). - Remember to always consider the orientation of the surface relative to the electric field when calculating electric flux.